In this paper we study, mainly numerically, stochastic pitchfork bifurcation. By stochastic bifurcation we mean that new invariant measures appear as parameters contained in random dynamical systems are varied. We also show, by example, that using computer algebra MAPLE one can calculate...

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the...

In this paper, using the theories and methods of ecology and ordinary differential equations, an ecological model with an impulsive control strategy and a distributed time delay is defined. Using the theory of the impulsive equation, small-amplitude perturbations, and comparative techniques, a...

This paper analyses the constant elasticity of volatility (CEV) model suggested by Chan et al. [K.C. Chan, G.A. Karolyi, F.A. Longstaff, A.B. Sanders, An empirical comparison of alternative models of the short-term interest rate, Journal of Finance 47 (1992) 1209–1227]. The CEV model without...

We show how to simulate Brownian motion not on a regular time grid, but on a regular spatial grid. That is, when it first hits points in δZ for some δ0. Central to our method is an algorithm for the exact simulation of τ, the first time Brownian motion hits ±1. This work is motivated by...

Stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Most...

In this paper, we investigate nonlinear adaptive–impulsive synchronization of chaotic systems. The core of adaptive–impulsive synchronization of chaotic systems is to design suitable nonlinear adaptive–impulsive controllers to attain certain aims. Based on invariant principle of impulsive...

The response of a two-degree-of-freedom system with quadratic coupling under a modulated amplitude sinusoidal excitation is studied and solved. The method of multiple scale perturbation technique is applied to obtain the bifurcation response equation near the combination resonance case in the...

This paper proposes a simple adaptive synchronization method for a chaotic permanent magnet synchronous motor (PMSM). Convergence of the closed-loop system responses is shown by using a Lyapunov function. The proposed adaptive synchronization method does not require the restrictive assumption of...

A nonlinear stability analysis using a multiple-scales perturbation procedure is performed for the instability of two layers of immiscible, strongly anisotropic, magnetized, inviscid, arbitrarily compressible fluids in relative motion. Such configurations are of relevance in a variety of...