In this work, we investigate the dynamical behaviors of the rational difference equationwith arbitrary initial conditions, where A, B, and C are arbitrary constants. A general solution is obtained. Asymptotic behavior and asymptotic stability of the equilibrium points are investigated. The existence of the periodic solutions is discussed. Numerical simulations are carried out to verify the analytical results.
This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.
In this paper, an adaptive control scheme is developed to study the add order synchronization and the add order antisynchronization behavior between two different dimensional fractional order chaotic systems with fully uncertain parameters. This design of adaptive controller is based on the Lyapunov stability theory. Analytic expression for the controller with its adaptive laws of parameters is shown. The adaptive add order synchronization and add order anti-synchronization between two fractional order chaotic systems are used to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are used to verify the results.
In this paper, we study the weak convergence of "Leray-type" solutions of a magneto-hydro-dynamic systems. The proofs are based on weak compactness arguments and linear algebra methods.
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