Related papers: Cross-diffusion Modeling in Macroeconomics
In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical…
In this note we present a study of the solutions associated to a particular spatial extension of the Rosenzweig-MacArthur model for predator and prey. The analysis presented here shows that positive steady state solutions emerge via a…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
Switching model with one predator and two prey species is considered. The prey species have the ability of group defence. Therefore, the predator will be attracted towards that habitat where prey are less in number. The stability analysis…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
We present analytic and numerical results for two models, namely the minority model and the bar-attendance model, which offer simple paradigms for a competitive marketplace. Both models feature heterogeneous agents with bounded rationality…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
A simple computer simulation model of a closed market on a fixed network with free flow of goods and money is introduced. The model contains only two variables : the amount of goods and money beside the size of the system. An initially flat…
In this manuscript, we consider temporal and spatio-temporal modified Holling-Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator.…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the…
In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain.…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
In this paper, we present the possibility of using the Ising like models to explain by Statistical Physics means the connection between the financial discontinuities (herd behavior, bubbles, crashes) and "critical points" in physical of…
The global markets provide enterprises with selling opportunities and challenges in stabilizing operational strategies. From the perspective of production management, it is important to improve the profitability of an enterprise by…
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the…