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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 not easy difficulties is to appreciate how a bunch of cells or sensible devices, each one exhibiting complex nonlinear dynamic phenomena, can have interaction with each other to supply a coherent reaction on a better organizational point.

This ebook is a advisor to the attention-grabbing new notion of chaotic synchronization. the subjects coated diversity from transverse balance and riddled basins of allure 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 subject matters taken care of within the publication are on-off intermittency and the function of the soaking up and combined soaking up components, periodic orbit threshold concept, the impact of a small parameter mismatch, and assorted mechanisms for chaotic section synchronization.

The organic examples contain synchronization of the bursting habit of coupled insulin-producing beta cells, chaotic section synchronization within the strain and movement law of neighboring practical 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 platforms; Coupled Pancreatic Cells; Chaotic section Synchronization; inhabitants Dynamic structures; Clustering of worldwide Maps; Interacting Nephrons; Coherence Resonance Oscillators.

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46] P. A. Samuelson, Interactions Between the Multiplier Analysis and the Principle of Acceleration, The Review of Economic Statistics 2 1 , 75-78 (1939). [47] R. Goodwin, The Nonlinear Accelerator and the Persistence of Business Cycles, Econometrica 19, 1-17 (1951). W. Forrester, Industrial Dynamics (MIT Press, Cambridge, 1961). [49] H. Simon, The Sciences of the Artificial (MIT Press, Cambridge, 1969). L. Meadows, Dynamics of Commodity Production Cycles (Wright-Allen Press, Cambridge, 1970).

These parameters are specified so that #(1) = 1, g'(l) = 1, and g"(l) = 0. Furthermore lim u ^ 0 0 g(u) = f3 and lim^-oo g(u) = 0. Note that g(u) has a neutral interval around the equilibrium point (u = 1) where actual orders equal desired orders. The desired capital stock fc*- is proportional to the desired production rate x* with a constant capital-output ratio. Thus, it is implicitly assumed that the relative prices of the two types of capital are constant, so there is no variation in desired factor proportions.

1) for a cycle Pn of any period n in the diagonal will be derived in Chapter 3. 3. The two generic forms for the repelling tongues that develop from each point on a transversely unstable periodic cycle. Note that these tongues do not have sharp boundaries. They are made up by bundles of trajectories that happen to fall in the neighborhood of P. Let us now suppose that the fixed point P{XQ,XQ) belongs to the chaotic attractor A on the main diagonal, and that A has an (ergodic) absolutely continuous invariant measure on it.

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