## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

The current paper is devoted to the ergodicity of stochastic coupled fractional Ginzburg-Landau equations driven by $α$-stable noise on the Torus $\mathbb{T}$. By the maximal inequality for stochastic $α$-stable convolution and commutator estimates, the well-posedness of the mild solution for stochastic coupled fractional Ginzburg-Landau equations is established. Due to the discontinuous trajectories and non-Lipschitz nonlinear term, the existence and uniqueness of the invariant measures are obtained by the strong Feller property and the accessibility to zero.

The existence and uniqueness of solutions satisfying energy equality is proved for non-autonomous FitzHugh-Nagumo system on a special time-varying domain which is a (possibly non-smooth) domain expanding with time. By constructing a suitable penalty function for the two cases respectively, we establish the existence of a pullback attractor for non-autonomous FitzHugh-Nagumo system on a special time-varying domain.

In this paper, a general class of nonlinear dynamical systems described by retarded differential equations with discontinuous right-hand sides is considered. Under the extended Filippov-framework, we investigate some basic stability problems for retarded differential inclusions (RDI) with given initial conditions by using the generalized Lyapunov-Razumikhin method. Comparing with the previous work, the main results given in this paper show that the Lyapunov-Razumikhin function is allowed to have a indefinite or positive definite derivative for almost everywhere along the solution trajectories of RDI. However, in most of the existing literature, the derivative (if it exists) of Lyapunov-Razumikhin function is required to be negative or semi-negative definite for almost everywhere. In addition, the Lyapunov-Razumikhin function in this paper is allowed to be non-smooth. To deal with the stability, we also drop the specific condition that the Lyapunov-Razumikhin function should have an infinitesimal upper limit. Finally, we apply the proposed Razumikhin techniques to handle the stability or stabilization control of discontinuous time-delayed neural networks. Meanwhile, we present two examples to demonstrate the effectiveness of the developed method.

We present the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein-Ulenbeck equations, and establish the existence and uniqueness of mild solutions for time fractional and space nonlocal stochastic Boussinesq equations driven by Gaussian white noise.

This paper is devoted to the invasion traveling wave solutions for a temporally discrete delayed reaction-diffusion competitive system. The existence of invasion traveling wave solutions is established by using Schauder's fixed point Theorem. Ikeharaś theorem is applied to show the asymptotic behaviors. We further investigate the monotonicity and uniqueness invasion traveling waves with the help of sliding method and strong maximum principle.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]