Complexity And Evolution Of Dissipative Systems An Analytical Approach Sergey Vakulenko by Sergey Vakulenko 9783110268287, 9783110266481, 9783110268294, 3110268280, 3110266482, 3110268299 instant download after payment.

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.

• Based on new basic results
• Advanced methods in bioinformatics and mathematical biology
• A new, general and mathematically rigorous approach to a large class of networks and spatially extended systems important in applications