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The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises.…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$…
In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the…
Almost sure asymptotic stabilization of a discrete-time switched stochastic system is investigated. Information on the active operation mode of the switched system is assumed to be available for control purposes only at random time…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…
Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small…
A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…
This paper presents an SIR epidemic model with two different types of perturbations: white and L\'evy noises. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. We use the comparison…
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Such asymptotic regime occurs when the system starts from…
For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to…
We investigate the asymptotic behaviour of a reduced {\alpha}{\Omega}-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the {\alpha}-effect results in a system with state-dependent stochastic perturbations.…