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We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic solutions are obtained. In particular,…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…
In this article, we analyse the non-local model : $\partial$ t U (t, x) = J $\star$ U (t, x) -- U (t, x) + f (x -- ct, U (t, x)) for t > 0, and x $\in$ R, where J is a positive continuous dispersal kernel and f (x, s) is a heterogeneous KPP…
Cooperative dynamics are common in ecology and population dynamics. However, their commonly high degree of complexity with a large number of coupled degrees of freedom renders them difficult to analyse. Here we present a graph-theoretical…
In this paper, we examine both stability and sustainability of a network-based model of natural resource consumption. Stability is studied from a dynamical systems perspective, though we argue that sustainability is a fundamentally…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
In this paper, we study the simultaneous stability problem of a finite number of locally inter-connected linear subsystems under practical constraints, including asynchronous and aperiodic sampling, time-varying delays, and measurement…
Let $X$ be a max-stable random vector with positive continuous density. It is proved that the conditional independence of any collection of disjoint sub-vectors of $X$ given the remaining components implies their joint independence. We…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…
This paper studies deterministic consensus networks with discrete-time dynamics under persistent flows and non-reciprocal agent interactions. An arc describing the interaction strength between two agents is said to be persistent if its…
In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces…
The stage of evolution is the population of reproducing individuals. The structure of the population is know to affect the dynamics and outcome of evolutionary processes, but analytical results for generic random structures have been…