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Abstract |
The talk will discuss three different modeling approaches indescribing complex systems at microscopic (trajectory-based), macroscopic (statistics-based), or mesoscopic (distribution-based) levels. With particular attentions paying to mesoscopic models as white-noise perturbed systems of ordinary differential equations, new existence and non-existence results of stationary measures of the corresponding diffusion processes will be presented by relaxing the notion of Lyapunov functions. Limiting behaviors of stationary measures will be discussed along with applications to problems of stochastic stability and bifurcations. Relating to the origin of ergodic theory, characterization of limiting Gibb's measures will be given in responding to the desired ergodicity of isolated particle systems under thermodynamics limits. |
