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This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
In the Vlasov-Poisson equation, every configuration which is homogeneous in space provides a stationary solution. Penrose gave in 1960 a criterion for such a configuration to be linearly unstable. While this criterion makes sense in a…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
We consider a non-linear stochastic wave equation driven by space-time white noise in dimension 1. First of all, we state some results about the intermittency of the solution, which have only been carefully studied in some particular cases…
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…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…
In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in $\mathbb{R}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the…
For a pendulum suspended below a vibrating block with white noise forcing, the solution in which the pendulum remains vertical is called the single mode solution. When this solution becomes unstable there is energy transfer from the block…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
We examine stochastic reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{A} u(t,x) + f(u(t,x)) + \sigma(u(t,x))\dot{W}(t,x)$ and provide sufficient conditions on the reaction term and multiplicative noise…
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 consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
We prove optimality principles for semicontinuous bounded viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle…
In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly…
We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…