Titlebook: Replication of Chaos in Neural Networks, Economics and Physics; Marat Akhmet,Mehmet Onur Fen Book 2016 The Editor(s) (if applicable) and T

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,Replication of Continuous Chaos About?Equilibria,concept, since it helps us to describe in the most general form the expansion of chaos, which is not only an enlargement of the dimension of chaotic systems, but also saving properties of chaos during the extension.

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Introduction, the global properties of solutions (Devaney, An Introduction to Chaotic Dynamical Systems, 1989) [.]. His discovery of the homoclinic orbits figures prominently in the studies of chaotic dynamical systems. Poincaré first encountered the presence of homoclinic orbits in the three-body problem of cel

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,Replication of Continuous Chaos About?Equilibria,ums. This is why we start with perturbation of linear systems with constant coefficients and globally asymptotically stable equilibriums. In this chapter, we introduce chaotic sets of functions, the generator and replicator of chaos, precise description of ingredients for Devaney and Li–Yorke chaos

Ancillary

Chaos Extension in Hyperbolic Systems,Devaney and Li–Yorke is taken into account for unidirectionally coupled systems. The rigorously proved results are supported by simulations. A method for controlling the extended chaos is also presented.

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領(lǐng)袖氣質(zhì)

Chaotification of Impulsive Systems,orke by implementing chaotic perturbations. An impulsive Duffing oscillator is used to show the effectiveness of our technique, and simulations that support the theoretical results are depicted. Moreover, a procedure to stabilize the unstable periodic solutions is proposed.

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Mawkish

Book 2016al and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approa