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Focusing on hybrid diffusion dynamics involving continuous dynamics as wellas discrete events, this article investigates the explicit approximations fornonlinear switching diffusion systems modulated by a Markov chain. Differentkinds of easily implementable explicit schemes have been proposed toapproximate the dynamical behaviors of switching diffusion systems with localLipschitz continuous drift and diffusion coefficients in both finite andinfinite intervals. Without additional restriction conditions except thosewhich guarantee the exact solutions posses their dynamical properties, thenumerical solutions converge strongly to the exact solutions in finite horizon,moreover, realize the approximation of long-time dynamical properties includingthe moment boundedness, stability and ergodicity. Some simulations and examplesare provided to support the theoretical results and demonstrate the validity ofthe approach.

Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons