Mean Evolutionary Dynamics for Stochastically Switching Environments

Stochastically Perturbed Sliding Motion in Piecewise-Smooth Systems

Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effects of small-amplitude, additive, white Gaussian noise on stable sliding motion. For equations that are static in directions parallel to the switching manifold, the distance of orbits from the switching manifold approaches a quasi-steady-state density. From this density we calculate the mean and variance for the near sliding solution. Numerical results of a relay control system reveal that the noise may significantly a…

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwit…

具有随机切换拓扑和时滞的离散时间多智能体网络中的一致性与同步

Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays

针对时变拓扑和时滞的多智能体网络，研究一致性算法的稳定性，证明在自环无延迟条件下网络达到一致，在自环有延迟且满足特定整数模式时算法可能同步到周期轨迹。

大但有限策略切换速率对疫苗接种进化博弈影响的几何分析

A geometric analysis of the impact of large but finite switching rates on vaccination evolutionary games

本文研究快速观点切换下疫苗接种进化博弈与流行病传播的双尺度耦合模型，提出切换依赖发病率的SIR博弈框架，并用几何奇异摄动理论分析，揭示准稳态近似的临界性问题。

Eco-Evolutionary Dynamics of Bimatrix Games

Feedbacks between strategies and the environment are common in social-ecological, evolutionary-ecological, and even psychological-economic systems. Utilizing common resources is always a dilemma for community members, like tragedy of the commons. Here we consider replicator dynamics with feedback-evolving games, where the payoffs switch between two different matrices. Although each payoff matrix on its own represents an environment where cooperators and defectors can't coexist stably, we show that it's possible to design appropriate switching control laws and achieve persistent oscillations of…

非线性公共物品博弈在动态环境中

Nonlinear Public Goods Game in Dynamical Environments

本文提出一种动态环境反馈机制的非线性公共物品博弈模型，揭示环境反馈、非线性效应和随机性对合作行为和系统动态的影响。