相关论文: Equilibrium in a large Lotka-Volterra system with …
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and…
Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The…
In this paper the problems of integrable and linearizable Lotka-Volterra equations with $(\delta:-3 \delta:\delta)$-resonance are studied. The necessary conditions for both problems are obtained in the case when $\delta=1$ and it's…
In the study of equilibrium solutions for partial differential equations there are so many equilibria that one cannot hope to find them all. Therefore one usually concentrates on finding individual branches of equilibrium solutions. On the…
Many complex systems share two characteristics: 1) they are stochastic in nature, and 2) they are characterized by a large number of factors. At the same time, various natural complex systems appear to have two types of intertwined…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for…
There is a renewed interest in the derivation of statistical mechanics from the dynamics of closed quantum systems. A central part of this program is to understand how far-from-equilibrium closed quantum system can behave as if relaxing to…
This paper primarily discusses the dynamical properties of a class of Lotka-Volterra models featuring the Allee effect and interspecific competition within the predator population. The constructed models employ Holling II and Holling I…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
In this work we consider a simple, approximate, tending toward exact, solution of the system of two usual Lotka-Volterra differential equations. Given solution is obtained by an iterative method. In any finite approximation order of this…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
The state space is a fundamental concept for describing the trajectory of a dynamic system. Depending on its form, it can highlight certain changes over time while ignoring others. This is particularly the case for the spaces associated…
We investigate cyclic dominance models and their extensions to both network systems and reaction-diffusion frameworks. Using linear stability analysis, we establish the relationship between the stability of synchronized states in network…
The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have…
A parameter-dependent class of Hamiltonian (generalized) Lotka-Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cases according to particular choices of the parameters. We…
In the paper we consider a system of differential equations with two delays describing plankton--fish interaction. We study stability of the equilibrium point corresponding to the presence of phytoplankton and zooplankton in the system and…
We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…