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El. knyga: Complexity and Evolution of Dissipative Systems: An Analytical Approach

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Focusing on mathematical methods for dissipative system complexity and mathematical biology, Vakulenko (mechanical engineering, Russian Academy of Sciences) considers the problem of the emergence of complexity in dissipative systems and chaos, stability, and evolution for genetic networks. The second problem goes back to Darwin asking how a gradual evolution can produce complex special organs functioning in a correct manner. Maybe, he suggests, biological systems are not as complex as they appear. He covers complex dynamics in neural and genetic networks; complex patterns and attractors for reaction-diffusion systems; and random perturbations, evolution, and complexity. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)

This book focusses ondynamic complexity of neural and genetic networks, reaction diffusion systems and equations of fluid dynamics.It considersviability problems for such systems and discusses an interesting hypothesis of M. Gromov andA. Carbone on biological evolution.Several applications are considered.

Complexity and evolution of spatially extended systems: analytical approach

Chapter 1: Introduction

  • Dynamical systems
  • Attractors
  • Strange attractors
  • Neural and genetic networks
  • Reaction diffusion systems
  • Systems with random perturbations and Gromov-Carbone problem

Chapter 2: Method to control dynamics: Invariant manifolds, realization of vector fields

  • Invariant manifolds
  • Method of realization of vector fields
  • Control of attractor and inertial dynamics for neural networks

Chapter 3: Complexity of patterns and attractors in genetic networks Centralized networks and attractor complexity in such network

  • A connection with computational problems, Turing machines and finite automatons
  • Graph theory, graph growth and computational power of neural and genetical networks
  • Mathematical model that shows how positional information can be transformed into body plan of multicellular organism
  • Applications to TF- microRNA networks. Bifurcation complexity in networks

Chapter 4: Viability problem, Robustness under noise and evolution

  • Here we consider neural and genetic networks under large random perturbations
  • Viability problem
  • We show that network should evolve to be viable, and network complexity should increase
  • A connection with graph growth theory (Erdos-Renyi, Albert-Barabasi)
  • Relation between robustness, attractor complexity and functioning speed
  • Why Stalin and Putin's empires fall (as a simple illustration)
  • The Kolmogorov complexity of multicellular organisms and genetic codes: nontrivial connections
  • Robustness of multicellular organisms (Drosophila as an example)
  • A connection with the Hopfield system

Chapter 5: Complexity of attractors for reaction diffusion systems and systems with convection

  • Existence of chemical waves with complex fronts
  • Existence of complicated attractors for reaction diffusion systems
  • Applications to Ginzburg Landau systems and natural computing
  • Existence of complicated attractors for Navier Stokes equations
S. Vakulenko, Petersburg State University of Technology and Design, Russian Academy of Sciences, Saint Petersburg.
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Pastovi nuoroda: https://www.kriso.lt/db/97831102682872e.html
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