相关论文: On the Random Dynamics of Volterra Quadratic Opera…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
This paper studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a…
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating…
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition. Given a random contracting potential $\varphi$…
It is well-known that random attractors of a random dynamical system are generally not unique. It was shown in recent work by Hans Crauel and the author that if there exist more than one pullback or weak random attractor which attracts a…
We study the global stability of generalized Lotka-Volterra systems with generalized polynomial right-hand side, without restrictions on the number of variables or the polynomial degree, including negative and non-integer degree. We…
The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…
We show that attractive, translation invariant, one-dimensional spin systems started from the unit step function possess the following basic property. At any time, the entire configuration from a point onward is stochastically decreasing…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
We consider a new subclass of quadratic stochastic (evolutionary) operators on the simplex indexed by a finite Abelian group G with heredity law \mu. With the help of the notion of s(\mu)-invariant subgroups, where s(\mu) denotes the…
In this short note we study a dynamical system generated by a two-parametric quadratic operator mapping 3-dimensional simplex to itself. This is an evolution operator of the frequencies of gametes in a two-locus system. We find the set of…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
The paper is devoted to the study of the dynamical behavior of the solutions of stochastic FitzHugh-Nagumo lattice equations, driven by fractional Brownian motions, with Hurst parameter greater than $1/2$. Under some usual dissipativity…
We present some analytical results for the stochastic sandpile model, studied earlier by Manna. In this model, the operators corresponding to particle addition at different sites commute. The eigenvalues of operators satisfy a system of…
We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based…
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of…
We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
The paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite…