Preface |
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vii | |
Contributors |
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xi | |
I Introductory Course |
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1 | (168) |
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Dynamic Phenomena in Cells |
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3 | (18) |
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Scope of Cellular Dynamics |
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3 | (5) |
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Computational Modeling in Biology |
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8 | (3) |
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Cartoons, Mechanisms, and Models |
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8 | (1) |
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9 | (1) |
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10 | (1) |
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A Simple Molecular Switch |
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11 | (2) |
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Solving and Analyzing Differential Equations |
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13 | (7) |
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Numerical Integration of Differential Equations |
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15 | (3) |
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Introduction to Numerical Packages |
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18 | (2) |
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20 | (1) |
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Voltage Gated Ionic Currents |
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21 | (32) |
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Basis of the Ionic Battery |
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23 | (4) |
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The Nernst Potential: Charge Balances Concentration |
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24 | (2) |
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The Resting Membrane Potential |
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26 | (1) |
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27 | (2) |
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Equations for Membrane Electrical Behavior |
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28 | (1) |
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Activation and Inactivation Gates |
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29 | (5) |
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Models of Voltage-Dependent Gating |
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29 | (2) |
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31 | (3) |
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Interacting Ion Channels: The Morris-Lecar Model |
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34 | (11) |
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36 | (2) |
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38 | (2) |
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Why Do Oscillations Occur? |
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40 | (3) |
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Excitability and Action Potentials |
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43 | (1) |
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Type I and Type II Spiking |
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44 | (1) |
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45 | (2) |
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FitzHugh-Nagumo Class Models |
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47 | (2) |
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49 | (1) |
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50 | (3) |
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53 | (24) |
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54 | (3) |
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57 | (8) |
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59 | (1) |
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60 | (2) |
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Rate of the GLUT Transporter |
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62 | (3) |
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The Na+/Glucose Cotransporter |
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65 | (5) |
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70 | (3) |
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73 | (3) |
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76 | (1) |
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Fast and Slow Time Scales |
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77 | (24) |
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The Rapid Equilibrium Approximation |
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78 | (4) |
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Asymptotic Analysis of Time Scales |
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82 | (1) |
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Glucose-Dependent Insulin Secretion |
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83 | (5) |
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88 | (2) |
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The Neuromuscular Junction |
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90 | (1) |
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The Inositol Trisphosphate (IP3) receptor |
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91 | (3) |
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Michaelis-Menten Kinetics |
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94 | (4) |
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98 | (3) |
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101 | (39) |
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Models of ER and PM Calcium Handling |
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102 | (5) |
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Flux Balance Equations with Rapid Buffering |
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103 | (3) |
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Expressions for the Fluxes |
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106 | (1) |
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Calcium Oscillations in the Bullfrog Sympathetic Ganglion Neuron |
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107 | (8) |
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Ryanodine Receptor Kinetics: The Keizer-Levine Model |
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108 | (3) |
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Bullfrog Sympathetic Ganglion Neuron Closed-Cell Model |
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111 | (2) |
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Bullfrog Sympathetic Ganglion Neuron Open-Cell Model |
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113 | (2) |
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The Pituitary Gonadotroph |
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115 | (13) |
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The ER Oscillator in a Closed Cell |
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116 | (6) |
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Open-Cell Model with Constant Calcium Influx |
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122 | (2) |
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The Plasma Membrane Oscillator |
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124 | (2) |
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Bursting Driven by the ER in the Full Model |
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126 | (2) |
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128 | (8) |
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129 | (4) |
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133 | (3) |
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136 | (4) |
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Intercellular Communication |
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140 | (29) |
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Electrical Coupling and Gap Junctions |
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141 | (5) |
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Synchronization of Two Oscillators |
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142 | (1) |
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Asynchrony Between Oscillators |
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143 | (1) |
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Cell Ensembles, Electrical Coupling Length Scale |
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144 | (2) |
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Synaptic Transmission Between Neurons |
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146 | (4) |
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Kinetics of Postsynaptic Current |
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147 | (1) |
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Synapses: Excitatory and Inhibitory; Fast and Slow |
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148 | (2) |
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When Synapses Might (or Might Not) Synchronize Active Cells |
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150 | (3) |
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Neural Circuits as Computational Devices |
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153 | (6) |
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159 | (6) |
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165 | (4) |
II Advanced Material |
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169 | (209) |
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171 | (27) |
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One-Dimensional Formulation |
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173 | (6) |
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Conservation in One Dimension |
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173 | (2) |
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175 | (1) |
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176 | (1) |
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177 | (1) |
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177 | (1) |
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Boundary and Initial Conditions |
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178 | (1) |
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Important Examples with Analytic Solutions |
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179 | (5) |
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Diffusion Through a Membrane |
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179 | (1) |
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Ion Flux Through a Channel |
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180 | (1) |
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181 | (1) |
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Diffusion in a Long Dendrite |
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181 | (2) |
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Diffusion into a Capillary |
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183 | (1) |
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Numerical Solution of the Diffusion Equation |
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184 | (2) |
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Multidimensional Problems |
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186 | (3) |
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Conservation Law in Multiple Dimensions |
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186 | (1) |
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Fick's Law in Multiple Dimensions |
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187 | (1) |
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Advection in Multiple Dimensions |
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188 | (1) |
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Boundary and Initial Conditions for Multiple Dimensions |
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188 | (1) |
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Diffusion in Multiple Dimensions: Symmetry |
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188 | (1) |
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Traveling Waves in Nonlinear Reaction-Diffusion Equations |
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189 | (6) |
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190 | (2) |
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Traveling Wave in the Fitzhugh-Nagumo Equations |
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192 | (3) |
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195 | (3) |
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Modeling Intracellular Calcium Waves and Sparks |
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198 | (32) |
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Microfluorometric Measurements |
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198 | (2) |
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A Model of the Fertilization Calcium Wave |
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200 | (2) |
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Including Calcium Buffers in Spatial Models |
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202 | (1) |
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The Effective Diffusion Coefficient |
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203 | (1) |
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Simulation of a Fertilization Calcium Wave |
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204 | (1) |
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Simulation of a Traveling Front |
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204 | (4) |
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Calcium Waves in the Immature Xenopus Oocycte |
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208 | (1) |
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Simulation of a Traveling Pulse |
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208 | (2) |
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Simulation of a Kinematic Wave |
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210 | (3) |
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Spark-Mediated Calcium Waves |
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213 | (1) |
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The Fire-Diffuse-Fire Model |
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214 | (6) |
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Modeling Localized Calcium Elevations |
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220 | (2) |
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Steady-State Localized Calcium Elevations |
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222 | (5) |
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The Steady-State Excess Buffer Approximation (EBA) |
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224 | (1) |
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The Steady-State Rapid Buffer Approximation (RBA) |
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225 | (1) |
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Complementarity of the Steady-State EBA and RBA |
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226 | (1) |
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227 | (3) |
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230 | (31) |
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Biochemical Kinetics and Feedback |
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232 | (4) |
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236 | (3) |
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Two-Component Oscillators Based on Autocatalysis |
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239 | (4) |
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Substrate-Depletion Oscillator |
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240 | (2) |
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Activator-Inhibitor Oscillator |
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242 | (1) |
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Three-Component Networks Without Autocatalysis |
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243 | (4) |
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Positive Feedback Loop and the Routh-Hurwitz Theorem |
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244 | (1) |
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Negative Feedback Oscillations |
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244 | (1) |
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244 | (3) |
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Time-Delayed Negative Feedback |
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247 | (3) |
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Distributed Time Lag and the Linear Chain Trick |
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248 | (1) |
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249 | (1) |
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250 | (5) |
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255 | (6) |
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261 | (24) |
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Physiology of the Cell Cycle in Eukaryotes |
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261 | (2) |
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Molecular Mechanisms of Cell Cycle Control |
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263 | (2) |
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A Toy Model of Start and Finish |
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265 | (4) |
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Hysteresis in the Interactions Between Cdk and APC |
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266 | (1) |
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Activation of the APC at Anaphase |
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267 | (2) |
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A Serious Model of the Budding Yeast Cell Cycle |
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269 | (4) |
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Cell Cycle Controls in Fission Yeast |
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273 | (3) |
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Checkpoints and Surveillance Mechanisms |
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276 | (1) |
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Division Controls in Egg Cells |
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276 | (2) |
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Growth and Division Controls in Metazoans |
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278 | (1) |
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Spontaneous Limit Cycle or Hysteresis Loop? |
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279 | (2) |
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281 | (4) |
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Modeling the Stochastic Gating of Ion Channels |
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285 | (35) |
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Single-Channel Gating and a Two-State Model |
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285 | (8) |
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Modeling Channel Gating as a Markov Process |
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286 | (2) |
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The Transition Probability Matrix |
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288 | (1) |
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289 | (1) |
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290 | (1) |
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Simulating Multiple Independent Channels |
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291 | (1) |
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292 | (1) |
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An Ensemble of Two-State Ion Channels |
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293 | (5) |
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Probability of Finding N Channels in the Open State |
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293 | (3) |
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The Average Number of Open Channels |
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296 | (1) |
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The Variance of the Number of Open Channels |
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297 | (1) |
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Fluctuations in Macroscopic Currents |
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298 | (4) |
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Modeling Fluctuations in Macroscopic Currents with Stochastic ODEs |
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302 | (5) |
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Langevin Equation for an Ensemble of Two-State Channels |
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304 | (2) |
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Fokker-Planck Equation for an Ensemble of Two-State Channels |
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306 | (1) |
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Membrane Voltage Fluctuations |
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307 | (4) |
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Membrane Voltage Fluctuations with an Ensemble of Two-State Channels |
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309 | (2) |
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Stochasticity and Discreteness in an Excitable-Membrane Model |
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311 | (6) |
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Phenomena Induced by Stochasticity and Discreteness |
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312 | (1) |
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The Ensemble Density Approach Applied to the Stochastic Morris-Lecar Model |
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313 | (1) |
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Langevin Formulation for the Stochastic Morris-Lecar Model |
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314 | (3) |
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317 | (3) |
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320 | (34) |
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Molecular Motions as Stochastic Processes |
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323 | (7) |
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Protein Motion as a Simple Random Walk |
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323 | (2) |
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325 | (2) |
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Sample Paths of Polymer Growth |
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327 | (2) |
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The Statistical Behavior of Polymer Growth |
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329 | (1) |
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Modeling Molecular Motions |
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330 | (5) |
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330 | (2) |
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Numerical Simulation of the Langevin Equation |
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332 | (1) |
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333 | (1) |
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334 | (1) |
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Modeling Chemical Reactions |
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335 | (3) |
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338 | (1) |
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Numerical Simulation of Protein Motion |
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339 | (6) |
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Numerical Algorithm that Preserves Detailed Balance |
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340 | (1) |
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341 | (1) |
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342 | (2) |
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344 | (1) |
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345 | (8) |
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345 | (1) |
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The Equipartition Theorem |
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345 | (1) |
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A Numerical Method for the Langevin Equation |
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346 | (1) |
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Some Connections with Thermodynamics |
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347 | (2) |
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Jumping Beans and Entropy |
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349 | (1) |
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350 | (1) |
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Jump Rates at an Absorbing Boundary |
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351 | (2) |
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353 | (1) |
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Molecular Motors: Examples |
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354 | (24) |
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Switching in the Bacterial Flagellar Motor |
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354 | (5) |
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A Motor Driven by a ``Flashing Potential'' |
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359 | (3) |
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The Polymerization Ratchet |
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362 | (2) |
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Simplified Model of the Fo Motor |
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364 | (10) |
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The Average Velocity of the Motor in the Limit of Fast Diffusion |
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366 | (3) |
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Brownian Ratchet vs. Power Stroke |
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369 | (1) |
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The Average Velocity of the Motor When Chemical Reactions Are as Fast as Diffusion |
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369 | (5) |
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374 | (2) |
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376 | (2) |
A Qualitative Analysis of Differential Equations |
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378 | (32) |
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Matrix and Vector Manipulation |
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379 | (1) |
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A Brief Review of Power Series |
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380 | (2) |
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382 | (6) |
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Solution of Systems of Linear ODEs |
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383 | (2) |
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Numerical Solutions of ODEs |
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385 | (1) |
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Eigenvalues and Eigenvectors |
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386 | (2) |
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388 | (7) |
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Stability of Linear Steady States |
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390 | (2) |
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Stability of a Nonlinear Steady States |
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392 | (3) |
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395 | (6) |
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Bifurcation at a Zero Eigenvalue |
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396 | (2) |
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Bifurcation at a Pair of Imaginary Eigenvalues |
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398 | (3) |
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401 | (7) |
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401 | (2) |
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403 | (2) |
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Singular Perturbation Theory |
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405 | (3) |
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408 | (2) |
B Solving and Analyzing Dynamical Systems Using XPPAUT |
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410 | (29) |
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Basics of Solving Ordinary Differential Equations |
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411 | (11) |
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411 | (1) |
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412 | (1) |
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413 | (1) |
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Solving the Equations, Graphing, and Plotting |
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414 | (2) |
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Saving and Printing Plots |
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416 | (2) |
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Changing Parameters and Initial Data |
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418 | (1) |
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Looking at the Numbers: The Data Viewer |
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419 | (1) |
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Saving and Restoring the State of Simulations |
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420 | (1) |
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Important Numerical Parameters |
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421 | (1) |
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Command Summary: The Basics |
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422 | (1) |
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Phase Planes and Nonlinear Equations |
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422 | (5) |
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423 | (1) |
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Nullclines and Fixed Points |
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423 | (3) |
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Command Summary: Phase Planes and Fixed Points |
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426 | (1) |
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Bifurcation and Continuation |
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427 | (5) |
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General Steps for Bifurcation Analysis |
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427 | (1) |
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Hopf Bifurcation in the FitzHugh-Nagumo Equations |
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428 | (2) |
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Hints for Computing Complete Bifurcation Diagrams |
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430 | (2) |
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Partial Differential Equations: The Method of Lines |
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432 | (2) |
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434 | (5) |
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A Simple Brownian Ratchet |
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434 | (1) |
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434 | (2) |
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436 | (3) |
C Numerical Algorithms |
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439 | (12) |
References |
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451 | (12) |
Index |
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463 | |