Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Abstract

In term of the global random attractors theory, global dynamics of nonlinear stochastic heat conduction driven by multiplicative white noise with a variable coefficient are investigated numerically. It is shown that global 𝒟-bifurcation, secondary global 𝒟-bifurcation and complex dynamical behavior occur in motion of the system with increasing the intensity of linear component in the heat source. Furthermore, the results obtained here indicate that Hasudorff dimension which is relevant to global Lyapunov exponent can be used to describe global dynamics of the associated system qualitatively.

Keywords

• nonlinear stochastic heat conduction
• global dynamics
• random invariant measure
• hausdorff dimension
• global lyapunov exponent