This work presents an adaptive gain fixed-time synchronization of a seven-term hyperchaotic 4D system, along with its analog circuitry realizations. To facilitate a simplistic circuit realization of the closedloop sy...
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This work presents an adaptive gain fixed-time synchronization of a seven-term hyperchaotic 4D system, along with its analog circuitry realizations. To facilitate a simplistic circuit realization of the closedloop system, the control design process initiates with the design of a novel, simplified fixed-time stability lemma that gives a lower convergence time, while being easier to compute. A nonlinear, fixed-time adaptive-gain nonsingular terminal sliding mode controller was then designed to synchronize the hyperchaotic 4D system. Theoretical analyses successfully achieved fixed-time synchronization, and computer simulations verified the achievement of zero-error convergence across all states within 1 second, irrespective of the initial conditions and even in the presence of significant parameter and disturbance changes. Analog circuitry implementations of the adaptive gain fixed-time chaotic synchronization configuration were realized using commercially available components, for instance, LF357 and AD633. The circuit equations were devised to replicate those used in the controller, with the goal of facilitating troubleshooting by ensuring simplicity. Electronics workability was tested using PSPICE simulation program. The results demonstrated that active synchronization was achieved in fixed time with less than 1% error across the states in the presence of disturbances. Finally, the developed fixed-time chaotic synchronization was applied to a secure communication system. The results indicate that the original and recovered messages exhibit a high degree of similarity to each other after a fixed duration of 1 second.
This work presents the finite-time synchronization of a new six-term chaotic system with only stable equilibria and its circuitry implementation. The chaotic system is designed in such a way that its complex dynamical...
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This work presents the finite-time synchronization of a new six-term chaotic system with only stable equilibria and its circuitry implementation. The chaotic system is designed in such a way that its complex dynamical behavior, including hidden attractors, can be adjusted through only one parameter, whilst allowing transformation to chaotic flows via invariant transformations. A finite-time chaotic synchronizer is designed via a nonsingular terminal integral backstepping sliding mode controller, with reduced theoretical finite-time convergence, and a modified sliding surface, to accommodate analog circuitry implementations. A comparison between the proposed controller against conventional integral backstepping sliding mode controller showed that active synchronization is achieved in finite time. Finally, analog circuitry implementation for both open-loop and closed-loop configurations is realized via commercially available active components such as LF357 and AD633. The descriptive circuitry equations for both configurations are designed to mimic the actual governing control equations for simplicity and ease of circuit troubleshooting. The workability of both configurations was tested in OrCAD PSpice. Results show that the master and slave systems were found to be in synchronization with less than 0.95% maximum errors.
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