Related papers: Asymptotic behavior of coupled dynamical systems w…
In this paper we study the asymptotic behaviour of solutions of a system of $N$ partial differential equations. When $N = 1$ the equation reduces to the Burgers equation and was studied by Hopf. We consider both the inviscid and viscous…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
In a previous paper [3] we have studied flows defined on polytopes, presenting a new method to encapsulate its asymptotic dynamics along the edge-vertex heteroclinic network. These results apply to the class of polymatrix replicator…
In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains…
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…
In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…
We study the continuous time dynamics of the Thermal Minority Game. We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with non-trivial random…
We consider the evolutionary dynamics of a cooperative game on an adaptive network, where the strategies of agents (cooperation or defection) feed back on their local interaction topology. While mutual cooperation is the social optimum,…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type equations in a bounded domain with periodic boundary conditions. The system is motivated by our study of grain boundary dynamics, especially under…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
In this paper, we investigate the convergence of asymptotic systems in non-autonomous Cohen--Grossberg neural network models, which include both infinite discrete time-varying and distributed delays. We derive stability results under…
The long-time asymptotic behavior is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time…
The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the…
In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
System of partial differential equations with a convolution terms and non-local nonlinearity describing oscillations of plate due to Berger approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and…
Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…