Abstract:In this paper, we use Lyapunov direct method to analyze two identical Memristors systems and synchronization phenomena were discussed. The designed controllers were capable of making the time derivative of the Lyapunov's negative definite functions where these results give guarantees of stability of the error dynamics at the origin and proved the results in form of theoretical and numerical ways. As the result, in both cases, one can see the synchronization phenomena.
The generalized Kuramoto–Sivashinsky equation arises frequently in engineering, physics, biology, chemistry, and applied mathematics, and because of its extensive applications, this important model has received much attention regarding obtaining numerical solutions. This article introduces a new hybrid technique based on nonpolynomial splines and finite differences for solving the Kuramoto–Sivashinsky equation approximately. Specifically, the truncation error is studied to examine the convergence order of the proposed scheme, some problems are given to show its viability and effectiveness, and the norm errors are determined to compare the current method with the analytic solution and some other methods from the literature.
This paper presents a dynamical and generalized synchronization (GS) of two dependent chaotic nonlinear advection‐diffusion‐reaction (ADR) processes with forcing term, which is unidirectionally coupled in the master‐slave configuration. By combining backward differentiation formula‐Spline (BDFS) scheme with the Lyapunov direct method, the GS is studied for designing controller function of the coupled nonlinear ADR equations without any linearization. The GS behaviors of the nonlinear coupled ADR problems are obtained to demonstrate the effectiveness and feasibility of the proposed technique without losing natural properties and reduce the computational difficulties on capturing numerical solutions at the low value of the viscosity coefficient. This technique utilizes the master configuration to monitor the synchronized motions. The nonlinear coupled model is described by the incompressible fluid flow coupled to thermal dynamics and motivated by the Boussinesq equations. Finally, simulation examples are presented to demonstrate the feasibility of the synchronization of the proposed model.
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