Synchronization of hyperchaotic Chen systems: a class of the adaptive control approach

Abstract

The synchronization of hyperchaotic Chen systems is considered. An adaptive synchronization approach and a cascade adaptive synchronization approach are presented to synchronize a drive system and a response system. By utilizing an adaptive controller based on the dynamic compensation mechanism, exact knowledge of the systems is not necessarily required, and the synchronous speed is controllable by tuning the controller parameters. Sufficient conditions for the asymptotic stability of the two synchronization schemes are derived. Numerical simulation results demonstrate that the adaptive synchronization scheme with four control inputs and the cascade adaptive synchronization scheme with only one control signal are effective and feasible in chaos synchronization of hyperchaotic systems.

Scattering and bound state solutions of the asymmetric Hulthén potential

“…ℓ-wave continuum states of the Schrödinger equation for the modified Morse potential have been studied by Wei et.al. [7] where they have obtained the normalized analytical radial wave functions and derived a corresponding calculation of phase shifts. Chen et.al.…”

Scattering States of l -Wave Schrödinger Equation with Modified Rosen—Morse Potential

“…The Morse and/or original Rosen-Morse potentials, [1−2] as the important molecular model potentials, have been widely studied due to its validity in describing the vibration of actual diatomic molecules especially for the lowest electronic states. [3] Nevertheless, due to the Morse and/or original Rosen-Morse potentials do not consider the inner-shell radii of two atoms, it is therefore that they encounter inevitably some problem in reproducing the experimental data for some molecule states such as 6 1 Π u state of 7 Li 2 molecule and X 3 Π state of SiC radical. [4−6] Very recently, in order to fit the effect of inner-shell radii of two atoms for diatomic molecules, [7] Zhang et al [4] proposed based on the original Rosen-Morse potential [2] a modified Rosen-Morse potential in the form of…”

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

“…Since Pecora and Carroll established a chaos synchronization scheme for two identical chaotic systems with different initial conditions, [25] chaos synchronization has attracted a great deal of interest. [26][27][28][29] Because fractional-order chaotic systems can describe many practical systems more accurately, their synchronization has also attracted the attention of many scholars, and some techniques have been used to synchronize fractional-order chaotic systems. [21,[30][31][32][33] In practical situations, parameter uncertainty and external disturbance for fractional-order chaotic systems exist widely.…”