Add to ORKGThis paper extends, by an alternative method, a result of Mao (Systems and Control Letters, 1994) which shows that solutions of nonlinear differential equations can be destabilised by noise. Here, we show that a linear noise can always destabilise a gen-eral even-dimensional functional differential equation, with bounded or unbounded delay, and illustrate the general results for linear problems. Key words: stochastic destabilisation, stochastic functional differential equation, Itô-Volterra equation, Volterra equation, Liapunov exponent, nonlinear system. 1991 MSC: 60H10, 34K2
First part of this thesis (chapters 1-5) studies the effect of small noise perturbations on delay di...
This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion...
Population systems are often subject to environmental noise, and our aim is to show that (surprising...
This paper extends, by an alternative method, a result of Mao (Systems and Control Letters, 1994) wh...
This paper extends, by an alternative method, a result of Mao (Systems and Con-trol Letters, 1994) w...
This paper considers the stabilisation and destabilisa- tion by a Brownian noise perturbation which ...
ABSTRACT. The existence and uniqueness of global solutions of a class of scalar stochastic functiona...
This paper considers the stabilisation and destabilisa- tion by a Brownian noise perturbation which ...
This paper studies the oscillatory properties of solutions of linear scalar stochastic delay differe...
Abstract. The characteristic equation for a linear delay differential equation (DDE) has count-ably ...
AbstractWhen the right-hand side of an ordinary differential equation (ODE in short) is not Lipschit...
This thesis concerns the asymptotic growth of solutions to nonlinear functional differential equatio...
This brief treats dynamical systems that involve delays and random disturbances. The study is motiva...
In this work we present examples of the effects of noise on the solution of a partial differential e...
Abstract. This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochast...
First part of this thesis (chapters 1-5) studies the effect of small noise perturbations on delay di...
This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion...
Population systems are often subject to environmental noise, and our aim is to show that (surprising...
This paper extends, by an alternative method, a result of Mao (Systems and Control Letters, 1994) wh...
This paper extends, by an alternative method, a result of Mao (Systems and Con-trol Letters, 1994) w...
This paper considers the stabilisation and destabilisa- tion by a Brownian noise perturbation which ...
ABSTRACT. The existence and uniqueness of global solutions of a class of scalar stochastic functiona...
This paper considers the stabilisation and destabilisa- tion by a Brownian noise perturbation which ...
This paper studies the oscillatory properties of solutions of linear scalar stochastic delay differe...
Abstract. The characteristic equation for a linear delay differential equation (DDE) has count-ably ...
AbstractWhen the right-hand side of an ordinary differential equation (ODE in short) is not Lipschit...
This thesis concerns the asymptotic growth of solutions to nonlinear functional differential equatio...
This brief treats dynamical systems that involve delays and random disturbances. The study is motiva...
In this work we present examples of the effects of noise on the solution of a partial differential e...
Abstract. This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochast...
First part of this thesis (chapters 1-5) studies the effect of small noise perturbations on delay di...
This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion...
Population systems are often subject to environmental noise, and our aim is to show that (surprising...