On the Random Non-Autonomous Logistic Equation with Time-Dependent Coefficients

Persistence and Extinction of a Non-autonomous Logistic Equation with Random Perturbation

Persistence and extinction of a randomized non-autonomous logistic equation is studied. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The critical number between weak persistence and extinction is obtained.

Exact solutions of the mKdV equation with time-dependent coefficients

In this paper, we study the time variable coefficient modified Korteweg-de Vries (mKdV) equation from group-theoretic point of view. We obtain Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary variable coefficients. Finally, the solitary ...

Stability of the Hartree equation with time-dependent coefficients

Some new results on the dynamical behavior of non-autonomous logistic system with random perturbation

In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have similar dynamic behave with the deterministic system, but if the noise is sufficiently large, it will spoil these nice properties. Furthermore, we introduce...

N-dimensional nonlinear Fokker-Planck equation with time-dependent coefficients.

An N-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized Gaussian function related to the Tsallis statistics. Furthermore, we show that a rich class of diffusive processes, including normal and anomalous ones, can be ob...