It is shown that automorphisms of some factors of type III , with 0 < 1, corresponding to Kolmogorov quantum dynamical systems of entropic type are strongly clustering.

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to N−1/5. The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigatio...

It is shown that automorphisms of some factors of type III , with 0 < 1, corresponding to Kolmogorov quantum dynamical systems of entropic type are strongly clustering.

It is shown that automorphisms of some factors of type III , with 0 < 1, corresponding to Kolmogorov quantum dynamical systems of entropic type are strongly clustering.

This work investigates the dynamics of competitive Kolmogorov systems formulated in a semi-Markov regime-switching framework. The conditional holding time each environmental regime is allowed to follow arbitrary probability distribution on nonnegative half-line sense approximations. Sharp sufficient conditions coexistence and exclusion species are established, case ...

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equ...