We extend two fundamental properties of positive linear time-invariant (LTI) systems to homogeneous cooperative systems. Specifically, we demonstrate that such systems are D-stable, meaning that global asymptotic stability is preserved under diagonal scaling. We also show that a delayed homogeneous cooperative system is globally asymptotically stable (GAS) for any non-negative delay if and only...

We investigate the global asymptotic stability and Naimark-Sacker bifurcation of the difference equation xn+1 = F bxnxn−1 + cxn−1 + f , n = 0, 1, . . . with non-negative parameters and nonnegative initial conditions x−1, x0 such that bx0x−1 + cx−1 +f > 0. By using fixed point theorem for monotone maps we find the region of parameters where the unique equilibrium is globally asymptotically stable.

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T -periodic logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T -periodic system with ti...

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM...

In this paper, a virus infection model with time delay and absorption is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using comparison arguments, it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity. When the ba...

A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number 0 R is calculated. It is shown that this number characterizes the disease transmission dynamics: if 0 1 R , there only exists the disease-free equilibrium which is globally asymptotically stable; if 0 1 R , there is a unique endemic equilibrium and the disease persists,...

This paper discussed a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is g...

A hepatitis B virus infection model with time delay is discussed. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is studied. By using comparison arguments, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproduction r...

A predictive control algorithm globally asymptotically stabilizing a class of input-saturated nonlinear cascaded systems is presented. The developed predictive control law, which is calculated off-line as an unconstrained direct state feedback using a discrete-time linear model, is applied to the plant by means of an iterative procedure. In this way, closed-loop stability is guaranteed without ...

To curb the impact and transmission of worms and virus for simple mass action incidence rate in computer networks, SI1I2RS (Susceptible, Infectious due to worm, Infectious due to virus, Recovered and Susceptible) model have been formed. Basic reproduction number, endemic equilibrium state and their stability are discussed for the simple mass action incidence. For locally and globally asymptotic...