Titlebook: Dissipative Structures and Chaos; Hazime Mori,Yoshiki Kuramoto Textbook 1998 Springer-Verlag Berlin Heidelberg 1998 Chaos.Chaotic Attracto

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A Representative Example of Dissipative Structureture of the governing laws, there are various external factors whose combined influence causes the behavior to become even more complex. For this reason, it is very important in an attempt to understand dissipative behavior that we carefully select a few model examples from the multitude and concent

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Reaction—Diffusion Systems and Interface Dynamicss based on amplitude equations are in general not suited to describe patterns peculiar to such ‘excitable’ systems because, while excitability originates in a particular property of global flow in phase space, amplitude equations are obtained by considering only local flow. In fact, BZ reaction syst

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Phase Dynamics the statement, “Slow degrees of freedom govern the dynamics of the system,” was extremely effective. In Chap. 2, the weakly unstable mode in the neighborhood of the bifurcation point served as the slow degree of freedom, while in Chap. 3 this was the concentration of the inhibiting substance presen

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Foundations of Reduction Theory derived phenomenologically. In the present chapter, we consider the theoretical foundation of perhaps the most important types of model equations considered in Part I, amplitude equations and phase equations. The degrees of freedom contained in the corresponding reduced equations are generally char

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Dynamics of Coupled Oscillator Systemsous media. In the present chapter we consider another important class of dissipative systems consisting of a large number of degrees of freedom, those composed of aggregates of isolated elements. A neural network consisting of intricately coupled excitable oscillators (neurons) is one example of suc

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Introductionnd unpredictable solutions - chaotic orbits - come to be widely understood as universal phenomena in nonlinear dynamical systems. As we understand it now, chaos can be thought of as the main cause of the diversity that we see displayed in Nature’s perpetually changing panorama.

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A Physical Approach to Chaos Almost any nonequilibrium open system will, when some bifurcation parameter characterizing the system is made sufficiently large, display chaotic behavior. It can be said that chaos is Nature’s universal dynamical form. Chaos is characterized by the coexistence of an infinite number of unstable per

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Bifurcation Phenomena of Dissipative Dynamical Systems of a bifurcation parameter can cause various saddle points to enter and leave attractors. Chaotic bifurcations result from the collision of an attractor with such points and their resultant inclusion into the attractor.