In this paper, the deterministic and stochastic SIRS epidemic models with nonlinear incidence are introduced and investigated. For deterministic system, the basic reproductive number R0 is obtained. Furthermore, if R0≤1, then the disease-free equilibrium is globally asymptotically stable and...

In this paper, a stochastic Lotka–Volterra competitive model with time-dependent delays is investigated. Sufficient conditions for global asymptotic stability of the positive equilibrium are established. The obtained result demonstrates that time-dependent delays have important impacts on the...

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis type functional response and logistic growth for predators. The deterministic model is already well-studied and we recall some important results here. We construct the stochastic model from the deterministic...

We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold...

We discuss the Landau theory for a nonlinear equation that can describe social changes, such as an influence of the social environment on individual. The models can explain why the minority can survive inside the majority population. It is described in terms of the complex intermittent clusters...

Epidemiological models with bilinear incidence rate λSI usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable non-trivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we...

We consider continuous-time Markov kinetics with a finite number of states and a positive equilibrium P∗. This class of systems is significantly wider than the systems with detailed balance. Nevertheless, we demonstrate that for an arbitrary probability distribution P and a general system...

In a recent paper [T. Wada, A.M. Scarfone, Phys. Lett. A 335 (2005) 351] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend these results to a system which is out...

Generalized entropies are studied as Lyapunov functions for the master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients), trace-form (the form of sum over the states), and additivity...

This paper regards the outer synchronization between two delay-coupled complex dynamical networks with nonidentical topological structures and a noise perturbation. Considering one network as the drive network and the other one as the response network, the drive–response system achieves...