… stability and some approaches used for analyzing bifurcation behavior of nonlinear stochastic
… of stochastic bifurcations, namely, the stochastic (i) Hopf, (ii) simple, and (iii) double-zero …

… D- and P-bifurcation In this paper we report on progress made in stochastic bifurcation theory …
of the theory, as laid down in Chapter 9 (Bifurcation Theory) of [1 J. We will only discuss …

… Hopf bifurcation. The analysis is carried out through the study of a noisy Duffing-van der Pol
oscillator which exhibits a Hopf bifurcation … the two concepts of stochastic bifurcation theory: …

We study an ordinary differential equation controlled by a stochastic process. We present
results on existence and uniqueness of solutions, on associated local times (Trotter and Ray–…

… the application of stochastic bifurcation theory faces many … stochastic model by introducing
a noisy fundamental price in a continuous-time framework. We then use stochastic bifurcation …

… of stochastic bifurcation, and shows the evidence of the destruction of Hopf bifurcation from
… a nonlinear mathematical model near the Hopf bifurcation, which may be derived from the …

… of stochastic bifurcations [2]. In this direction, large number of investigations has been devoted
to stochastic bifurcations and noise-induced transitions [3–14]. In stochastic systems, one …

… to stochastic gene regulation. In this paper, we present a simple unifying theory for stochastic
bifurcation … We study three biochemical network models that exhibit stochastic bifurcation: …

… In stochastic dynamics, bifurcation is related to the stochastic … Nonstationary stochastic
bifurcation (or Hopf stochastic bifurca… By stationary bifurcation we mean bifurcation of the steady …

… , stochastic optimal control strategy is the key concept and thus should be included in such
studies. In this article, a stochastic … optimum system for the delayed stochastic model. By using …