In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have similar dynamic behave with the deterministic system, but if the noise is sufficiently large, it will spoil these nice properties. Furthermore, we introduce...

Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transien...

The knowledge about higher brain centres in insects and how they affect the insect’s behaviour has increased significantly in recent years by theoretical and experimental investigations. Nowadays, a large body of evidence suggests that higher brain centres of insects are important for learning, short-term, longterm memory and play an important role for context generalisation (Bazhenof et al., 2...

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic LotkaVolterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not ...

Recent studies investigating feedbacks between evolution and ecology suggest that microevolution may affect community structure. Motivated by this, we use a quantitative genetics and LotkaVolterra framework to understand the impact of eco-evolutionary feedbacks on an intraguild predation community in which the intraguild predator evolves between a phenotype specialized for attacking its competi...

The theory of chaos is nowadays receiving a great deal of attention among social scientists. Many attempts are being made to offer a raeaningful interpretation and application of notions of chaos in social systems. The present paper aims to link chaos theory to spatial interaction analysis by focusing attention on the conditions under which a general utility function related to a dynamic logit ...

Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propos...

At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlook most aspects of transitions theory, for instance dimensions of heterogenou...

This paper is concerned with the following two-species LotkaVolterra competition-diffusion system in the three-dimensional spatial space { ∂ ∂t u1(x, t) = ∆u1(x, t) + u1(x, t) [1− u1(x, t)− k1u2(x, t)] , ∂ ∂t u2(x, t) = d∆u2(x, t) + ru2(x, t) [1− u2(x, t)− k2u1(x, t)] , where x ∈ R3 and t > 0. For the bistable case, namely k1, k2 > 1, it is well known that the system admits a one-dimensional mo...

A 3D competitive Lotka-Volterra equation with two limit cycles is constructed. Keywords-Lotka-Volterra equations, Competitive systems, Limit cycles, Hopf bifurcation. INTRODUCTION It is a classical result (due to Moisseev 1939 and/ or Bautin 1954, see [l, p. 213, Section 12, Example 71 or [2, 18.21) that 2D Lotka-Volterra equations cannot have limit cycles: if there is a periodic orbit, then th...