The paper considers some concept of uniform and nonuniform asymptotical growth and polynomial growth as particular cases of (h,k)-stability of evolution operators in Banach spaces. Some illustrating examples clarify the relations between these properties. 2000 Mathematics Subject Classification: 34D05, 34E05.

The shunting inhibitory cellular neural networks with continuously distributed delays and pseudo almost periodic coefficients are considered. First, we make a generalization of the Halanay inequality, and then establish some sufficient conditions for the existence and asymptotical stability of pseudo almost periodic solutions. Finally, a numerical simulation is presented to illustrate the theor...

A stochastic predator-prey system involving time-varying delays is considered. Some new sufficient conditions for existence, extinction and global asymptotical stability are obtained. It is interesting that the results are based on the variable delays, which is different from the previous work (the results are delay-independent). Some numerical simulations are introduced to support the analytic...

In this paper, asymptotical stability of genetic regulatory networks with interval time-varying delays is investigated. By choosing an appropriate new Lyapunov functional and employing convex combination method to estimate the derivative of the Lyapunov functional, some new delay-range-dependent and delay-derivativedependent/independent stability criteria are presented in terms of linear matrix...

We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled ...

This paper considers the robust stability bound problem of uncertain fractional-order systems. The system considered is subject either to a twonorm bounded uncertainty or to a infinity-norm bounded uncertainty. The robust stability bounds on the uncertainties are derived. The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order sys...

This paper investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative. By using the Mittag-Leffler function, Laplace transform and the Gronwall-Bellman lemma, one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in (0, 2). According to this theory,...

Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy is investigated. Four new sufficient conditions that guarantee the exponential stability of the impulsive evolution operator introduced by us are given. By virtue of exponential stability of the impulsive evolution operator, we present the existence, ...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...