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This paper investigates the global chaos synchronization of identical Liu-Su-Liu chaotic systems (2006) and non-identical Liu-Su-Liu chaotic system (2006) and Liu-Chen-Liu chaotic system (2007). In this paper, active nonlinear control method has been successfully applied to synchronize two identical Liu-Su-Liu chaotic systems and then to synchronize two different chaotic systems, viz. Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to synchronize Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Numerical simulations are also given to illustrate the proposed synchronization approach.

This paper investigates the state estimation of a stochastic model for the spread of HIV in mobile heterosexual population. The transmission of HIV model with the force of infection in the multiple patches is investigated for the varying population. In this paper, we introduce a novel concept of the observer model like a transmission of HIV model to estimate the spread of HIV in mobile heterosexual population. The boundedness and the equilibrium points have been found for the error state of observer model and original model. The global stability properties are analyzed by the concept of Lyapunav function. The stochastic model is introduced for the examination of the stochastic stability of the positive equilibrium. The stochastic and deterministic models of the system are compared and analyzed. Finally numerical examples and corresponding diagrams are presented to support the results.