Chaotic Synchronization: Applications to Living Systems by Erik Mosekilde

By Erik Mosekilde

Interacting chaotic oscillators are of curiosity in lots of components of physics, biology, and engineering. within the organic sciences, for example, one of many difficult difficulties is to appreciate how a gaggle of cells or useful devices, every one exhibiting advanced nonlinear dynamic phenomena, can engage with each other to supply a coherent reaction on a better organizational point.

This e-book is a advisor to the attention-grabbing new notion of chaotic synchronization. the themes lined variety from transverse balance and riddled basins of charm in a procedure of 2 coupled logistic maps over partial synchronization and clustering in structures of many chaotic oscillators, to noise-induced synchronization of coherence resonance oscillators. different subject matters taken care of within the ebook are on-off intermittency and the function of the soaking up and combined soaking up parts, periodic orbit threshold thought, the effect of a small parameter mismatch, and diversified mechanisms for chaotic part synchronization.

The organic examples contain synchronization of the bursting habit of coupled insulin-producing beta cells, chaotic part synchronization within the strain and move law of neighboring sensible devices of the kidney, and homoclinic transitions to part synchronization in microbiological reactors.

Contents: Coupled Nonlinear Oscillators; Transverse balance of Coupled Maps; Unfolding the Riddling Bifurcation; Time-Continuous platforms; Coupled Pancreatic Cells; Chaotic part Synchronization; inhabitants Dynamic structures; Clustering of worldwide Maps; Interacting Nephrons; Coherence Resonance Oscillators.

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19. ) Scenario 2 If the nonlinear mechanisms are too weak to restrict the motion to an absorbing area inside the basin of attraction for the synchronized state, the alternative is that most points leaving U%{A) diverge or go to another attractor. This can be an attracting point cycle, an invariant torus, or a chaotic attractor. On the other hand, provided that Ax < 0 the measure of the complementary set f/| C U$\U]j of points that are attracted to A and never leave Us normally approaches the measure of Us for 5 —> 0 [8, 9].

Other sources of coupling were ignored. The most obvious links are created by the price system. If, for instance, one type of capital is in short supply, one would expect the relative price of that factor to rise. To the extent that sectors can substitute one type of capital for another, one would expect demand for the relatively cheaper capital components to rise. In this way, the price system will cause local imbalances between order and capacity across the sectors to equalize, thus helping to bring the individual sectors into phase.

3, and in Sec. 4 we determine the bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the chaotic attractor. For one-band, two-band, and four-band chaotic dynamics we hereafter follow the changes that take place in the attractor and its basin of attraction under passage of the riddling and Transverse Stability of Coupled Maps 37 blowout bifurcations [26]. It is shown that the loss of weak stability does not necessarily affect the basin of attraction. Instead, the chaotic attractor may spontaneously break the symmetry and spread into the two-dimensional phase space.

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