Coexistence and exclusion of competitive Kolmogorov systems with semi-Markovian switching

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 coexistence, convergence rate transition unique stationary measure estimated. In weaker conditions, these results extend existing environment. Particularly, method proving exponential invariant for population models as random differential equations driven by process proposed.