MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

Adaptive Control and Synchronization of Uncertain Complex Networks

Recently, synchronization of complex networks has been a focus subject of technology fields. In this paper, we consider the adaptive control and synchronization of uncertain complex networks. By using the adaptive control techniques with the linear feedback updated law and the well-known invariant principle on dynamical system theory, some simple yet generic criteria are derived. Furthermore, the result is applied to typical chaotic cellular neural networks (CNN). Finally, numerical simulations are presented to demonstrate the feasibility and effectiveness of the proposed techniques.

Desynchronization of the Chaotic-Bursting Neuronal Ensemble Based on LaSalle Invariant Principle

In this paper, an adaptive control scheme is presented for the desynchronization of a neuronal population based on LaSalle invariant principle. This control can asymptotically stabilize the mean field of the popolation at a fixed point to achieve desynchronization. A realistic model described by Hindmarsh-Rose equations is chosen as our example. The simulation results demonstrate the effectiveness of the proposed control scheme.

Lyapunov Control of Quantum Systems with Impulsive Control Fields

We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.

Qualitative Analysis of a Ratio-Dependent Chemostat Model with Holling-(n+1) Type Functional Response

In this paper, the ratio-dependent chemostat model with Holling-(n+1) type functional response is considered. The model develops the Monod model and the ratio-dependent model. By use of the Poincar -Bendixson theory we prove the existence of limit cycle. Detailed qualitative analysis about the global asymptotic stability of its equilibria is carried out by using the Lyapunov-LaSalle invariant principle and the method of Dulac criterion.

Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustrate the effectiveness and feasibility of the proposed methods.

Global Dynamics of HIV Infection of CD4+T Cells and Macrophages

We study the global dynamics of an HIV infection model describing the interaction of the HIV with CD4+T cells and macrophages. The incidence rate of virus infection and the growth rate of the uninfected CD4+T cells and macrophages are given by general functions. We have incorporated two types of distributed delays into the model to account for the time delay between the time the uninfected cells are contacted by the virus particle and the time for the emission of infectious (matures) virus particles. We have established a set of conditions which are sufficient for the global stability of the steady states of the model. Using Lyapunov functionals and LaSalle's invariant principle, we have proven that if the basic reproduction numberR0is less than or equal to unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the infected steady state exists, then it is GAS.

Stabilization Control of Complex Dynamics of Light-Emitting Diode System Based on LaSalle Invariant Principle

Light-emitting diodes with optoelectronic feedback loop display complex sequences of periodic mixed mode oscillations and chaotic spiking. In this paper, we propose an adaptive control scheme for the stabilization of this complex dynamics, which is based on LaSalle invariant principle. The controller can asymptotically stabilize unstable equilibrium points of dynamical systems without explicit knowledge of the desired steady-state position. The simulation results demonstrate the effectiveness of the proposed control scheme.