相关论文: Persistence in extended dynamical systems
We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite…
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
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…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…