Complexity and Evolution of Dissipative Systems : An Analytical Approach
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| Title: | Complexity and Evolution of Dissipative Systems : An Analytical Approach |
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| Description: | This book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems. |
| Authors: | Sergey Vakulenko |
| Resource Type: | eBook. |
| Subjects: | Diffusion, Chaotic behavior in systems, System theory, Mathematical models, Energy dissipation, Mathematical physics, Attractors (Mathematics), Biophysics |
| Categories: | MATHEMATICS / Applied, MATHEMATICS / Differential Equations / General, MATHEMATICS / Discrete Mathematics, MATHEMATICS / Combinatorics, SCIENCE / Life Sciences / Biophysics, SCIENCE / Life Sciences / Molecular Biology, SCIENCE / Mechanics / Fluids |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | This book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems. |
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| ISBN: | 9783110266481 9783110268287 |
