Foundations of Synergetics II: Chaos and NoiseThe second edition of this volume has been extensively revised. A different version of Chap. 7, reflecting recent significant progress in understanding of spatiotempo ral chaos, is now provided. Much new material has been included in the sections dealing with intermittency in birth-death models and noise-induced phase transi tions. A new section on control of chaotic behavior has been added to Chap. 6. The subtitle of the volume has been changed to better reflect its contents. We acknowledge stimulating discussions with H. Haken and E. Scholl and are grateful to our colleagues M. Bar, D. Battogtokh, M. Eiswirth, M. Hildebrand, K. Krischer, and V. Tereshko for their comments and assistance. We thank M. Lubke for her help in producing new figures for this volume. Berlin and Moscow A. s. Mikhailov April 1996 A. Yu. Loskutov Preface to the First Edition This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise. |
Other editions - View all
Foundations of Synergetics II: Chaos and Noise Alexander S. Mikhailov,Alexander Yu. Loskutov Limited preview - 2013 |
Foundations of Synergetics II: Chaos and Noise Alexander S. Mikhailov,Alexander Yu. Loskutov No preview available - 2011 |
Foundations of Synergetics II: Complex Patterns Alexander Mikhailov,Alexander Yu. Loskutov No preview available - 2012 |
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A.S. Mikhailov amplitude approximately asymptotic behavior bifurcation boundary breeding centers chaos chaotic dynamics Chap coefficient complex consider control parameter correlation function correlation radius corresponding defects dependence described determined deterministic diffusion dimension dimensionality domains dynamical system eigenvalues elements estimate evolution explosion threshold exponentially finite fixed point fluctuations Fokker-Planck equation fractal Gaussian Ginzburg-Landau equation given Hence initial conditions integral intermittency internal noise interval iterative maps kbirth kdeath Lett limit cycle linear logistic map Lorenz model Lyapunov exponents medium nonlinear O₁ one-dimensional order parameter particles pattern periodic perturbation phase space phase trajectory phase transitions Phys plane Poincaré map population density probability distribution properties quasiperiodic motion random process reaction regime represents reproduction Sect sequence solution spatial spikes spiral wave Springer stable statistical stochastic differential equation strange attractor t₁ torus turbulence two-dimensional unstable variables vector volume Xn+1