By Sundarapandian Vaidyanathan, Christos Volos
This publication experiences at the most up-to-date advances and purposes of chaotic platforms. It comprises 25 contributed chapters by way of specialists who're really expert within the quite a few issues addressed during this publication. The chapters disguise a wide variety of subject matters of chaotic platforms corresponding to chaos, hyperchaos, jerk structures, hyperjerk structures, conservative and dissipative platforms, circulant chaotic platforms, multi-scroll chaotic platforms, finance chaotic approach, hugely chaotic platforms, chaos keep an eye on, chaos synchronization, circuit recognition and functions of chaos conception in safe communications, cellular robotic, memristors, mobile neural networks, and so forth. certain value used to be given to chapters delivering sensible ideas, modeling and novel keep an eye on equipment for the new study difficulties in chaos theory.
This ebook will function a reference ebook for graduate scholars and researchers with a uncomplicated wisdom of chaos conception and keep an eye on structures. The ensuing layout techniques at the chaotic structures are emphasised utilizing MATLAB software.
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Additional info for Advances and Applications in Chaotic Systems
Therefore, memristive system (13) is called a hyperjerk system because it involves time derivatives of a jerk function [45, 47]. 4. 5755. (17) 2 2 0 0 x3 Fig. 06, x2 (0) = 10−6 , x3 (0) = 0, and x4 (0) = 0. Here the initial condition of the input of the memristive device x2 (0) should be tiny to guarantee an appropriate value of the internal state variable of the memristive device. Figures 2, 3 and 4 illustrate the 2-D projections and 3-D projections of the new memristive system (13). −2 −2 −2 0 2 −2 0 x1 2 x4 x3 2 0 0 −2 −2 −2 0 −2 2 0 2 x1 x2 2 3 1 x Fig.
J Optoelectron Adv Mater Rapid Commun 8(11–12):1157–1163 47. Pham V-T, Jafari S, Volos ChK, Wang X, Golpayegani Mohammad Reza Hashemi S (2014) Is that really hidden? The presence of complex fixed-points in chaotic flows with no equilibria. Int J Bifurc Chaos 24(11):1450146 48. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824 49. Pikovsky AS (1984) On the interaction of strange attractors. Z Phys B—Condensed Matter 55:149–154 50. Pikovsky AS, Maistrenko YL (2003) Synchronization: theory and application.
4 The Case α = −2, β = 1 In the last case the parameters of the error function are chosen as α = −2 and β = 1. So, the attractor of the first coupled system has been enlarged again by factor two, while the attractor of the second coupled system has been inverted in regard to the first one, as it is shown in Fig. 45. 44 so as both of the coupled systems are in hyperchaotic state. This process is shown more clearly in the plots of the time series of x1 , y1 and x2 , y2 of Figs. 47 and 48. The phase portrait of y1 versus x1 in Fig.
Advances and Applications in Chaotic Systems by Sundarapandian Vaidyanathan, Christos Volos