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 bunch of cells or sensible devices, each one showing complex nonlinear dynamic phenomena, can engage with each other to supply a coherent reaction on the next organizational point.
This e-book is a consultant to the attention-grabbing new idea of chaotic synchronization. the subjects coated diversity from transverse balance and riddled basins of charm in a method 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 issues handled within the e-book are on-off intermittency and the position of the soaking up and combined soaking up parts, periodic orbit threshold idea, the effect of a small parameter mismatch, and diversified mechanisms for chaotic part synchronization.
The organic examples comprise synchronization of the bursting habit of coupled insulin-producing beta cells, chaotic part synchronization within the strain and circulate legislation of neighboring sensible devices of the kidney, and homoclinic transitions to section synchronization in microbiological reactors.
Contents: Coupled Nonlinear Oscillators; Transverse balance of Coupled Maps; Unfolding the Riddling Bifurcation; Time-Continuous structures; Coupled Pancreatic Cells; Chaotic part Synchronization; inhabitants Dynamic structures; Clustering of worldwide Maps; Interacting Nephrons; Coherence Resonance Oscillators.
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Extra info for Chaotic Synchronization: Applications to Living Systems
Our preliminary results demonstrate the importance of studying non-linear entrapment in the economy. The intricacies of such phenomena suggest that there is a vast unexplored domain of research in the area of economic cycles. We suppose that nonlinear interactions could play as large a role in shaping economic cycles as do the external random shocks on which much of mainstream business cycle theory relies. At the same time, our discussion points to the similarities in nature between the problems we meet in macroeconomic systems and in the biologically oriented problems discribed in other chapters of this book.
B. Stewart, Nonlinear Dynamics and Chaos (Wiley and Sons, Chichester, 1986). 10] L. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988). 11] G. Leng, Pulsatility in Neuroendocrine Systems (CRC Press, Boca Raton, 1988). -X. Li and A. Goldbeter, Frequency Specificity in Intercellular nication, Biophys. J. 55, 125-145 (1989). Commu- 13] F. J. M. Linkie, I. A. Downey, Menopausal Hot Flashes: Thermoregulatory, Cardiovascular, and Circulating Catecholamine and LH Changes, Maturitas 6, 31-43 (1984).
In each of these figures initial conditions leading to the chaotic attractor are plotted as gray points, and initial conditions leading to another attractor (or infinity) are left blank. , a little to the left of the region of asymptotic stability. In this region the synchronized period-6 cycle is transversely unstable, and the figure reveals the characteristic appearance of a globally riddled basin with a dense set of tongues with points that are repelled from the attractor emanating from the period-6 cycle and its preimages.