Chaotic Synchronization: Applications to Living Systems by Erik Mosekilde, Yuri Maistrenko, Dmitry Postnov, Iu. L.

By Erik Mosekilde, Yuri Maistrenko, Dmitry Postnov, Iu. L. Maistrenko

Interacting chaotic oscillators are of curiosity in lots of components of physics, biology, and engineering. within the organic sciences, for example, one of many not easy difficulties is to appreciate how a bunch of cells or practical devices, every one exhibiting complex nonlinear dynamic phenomena, can engage with each other to supply a coherent reaction on a better organizational point. This booklet is a advisor to the concept that of chaotic synchronization. the themes coated variety from transverse balance and riddled basins of allure in a approach of 2 coupled logistic maps, over partial synchronization and clustering in platforms of many chaotic oscillators, to noise-induced synchronization of coherence resonance oscillators. different themes taken care of within the booklet are on-off intermittency and the function of the soaking up and combined soaking up parts, periodic orbit threshold concept, the impression of a small parameter mismatch, and diverse mechanisms for chaotic section synchronization. The organic examples comprise synchronization of the bursting behaviour of coupled insulin-producing beta cells, chaotic section synchronization within the strain and circulate rules of neighbouring sensible devices of the kidney, and homoclinic transitions to section synchronization in microbiological reactors. This publication may be of curiosity to scholars and researchers drawn to utilising new ideas of chaotic synchronization and clustering to organic platforms.

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Extra resources for Chaotic Synchronization: Applications to Living Systems (World Scientific Series on Nonlinear Science, 42)

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24. 6 shows a scan of the transverse Lyapunov exponent X± as a function of the coupling parameter for a = ao- For this value of a, the individual map exhibits a one-band chaotic attractor consisting of two subintervals at the moment when they merge. 478, where Aj_ changes sign, are the blowout bifurcation points. In the interval between these points, the synchronized chaotic state is at least weakly stable. Outside this interval, A is a so-called chaotic saddle [23, 45]. Also indicated in Fig. 24 in which the chaotic attractor is asymptotically stable.

Chua, M. , L. Kocarev, and K. Eckert, Chaos Synchronization in Chua's Circuit. N. Madan (World Scientific, Singapore, 1993). S. Anishchenko, Dynamical Chaos - Models and Experiments. Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific, Singapore, 1995). E. Rossler, An Equation for Continuous Chaos, Phys. Lett. A 57, 397398 (1976). [46] P. A. Samuelson, Interactions Between the Multiplier Analysis and the Principle of Acceleration, The Review of Economic Statistics 2 1 , 75-78 (1939).

From the information in Fig. 5 we can therefore determine the regions of asymptotic stability for the synchronized chaotic attractor in each of the intervals ai < a < ao and ao < a. The first of these regions is bounded on both sides by the transverse destabilization of the period-2 cycle which occurs before destabilization of the period-8 and period-4 cycles. For higher values of a, destabilization of the period-6 cycle limits the region of asymptotic stability for the synchronized chaotic attractor, and there is also a region in parameter space where destabilization of the period-4 cycle is the first to take place.

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