Abstract
The principal target of this work is to introduce and examine a novel kind of complex synchronization. This sort may be called complex anti-synchronization. There are surprising properties of complex anti-synchronization that do not exist in the writing, for example, (1) this sort of synchronization can dissect just for complex nonlinear frameworks. (2) The complex anti-synchronization contains or connects two sorts of synchronizations (anti-synchronization and complete synchronization). Anti-synchronization happens between the real part of main framework and the imaginary part of the slave framework, although complete synchronization accomplishes between the real part of slave framework and the imaginary part of the main framework. (3) In complex anti-synchronization, the attractors of the essential and slave structures are moving symmetrical to each other with a similar structure. (4) The state variable of the standard framework synchronizes with an other state variable of the slave structure. An explanation of complex anti-synchronization is presented for two indistinguishable chaotic complex nonlinear frameworks. In view of the Lyapunov function, a plan is intended to accomplish complex anti-synchronization of disordered or chaotic attractors of these frameworks. The effectiveness of the obtained results is outlined by a reenactment illustration. Numerical outcomes are plotted to show state variable, modulus errors, phase errors and the development of the attractors of these chaotic frameworks after synchronization to demonstrate that complex anti-synchronization is accomplished.
Highlights
Nonlinear deterministic dynamical frameworks are pervasive in nature and are outstanding for their unusual property of delicate reliance on introductory conditions which offers ascend to their worldly unpredictability and obvious arbitrariness
Anti-synchronization happens between the real part of main framework and the imaginary part of the slave framework, complete synchronization accomplishes between the real part of slave framework and the imaginary part of the main framework
Numerical outcomes are plotted to show state variable, modulus errors, phase errors and the development of the attractors of these chaotic frameworks after synchronization to demonstrate that complex anti-synchronization is accomplished
Summary
Nonlinear deterministic dynamical frameworks are pervasive in nature and are outstanding for their unusual property of delicate reliance on introductory conditions which offers ascend to their worldly unpredictability and obvious arbitrariness. We study the description of CAS of two same structures of the shape [1] with specific parameters This kind of synchronization can be looked into for chaos and hyperchaos complex nonlinear structures figuratively speaking. We study two indistinguishable disorganized complicated nonlinear structures of the shape [1]; one is the main structure (we act the main model including the index (m)) as x_ m = x_ rm + jx_ imm = Fxm + FðxmÞ z_ = gðx, x, zÞ ð3Þ likewise, the other is the controlled slave structure (including index s) as x_ s = x_ rs + jx_ ism = Fxs + FðxsÞ + L ð4Þ such that the added element complex controller L = 1⁄2L1, L2, . Pair joined complex dynamical structures in a main-slave arrangement may display CAS if the vector of the unpredictable mistake or error function r define as.
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