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The theory of reaction-diffusion waves begins in the 1930s with the works in population dynamics, combustion theory and chemical kinetics. At the present time, it is a well developed area of research which includes qualitative properties of travelling waves for the scalar reaction-diffusion equation and for system of equations, complex nonlinear dynamics,(More)
de Jager et al. (Reports, 24 June 2011, p. 1551) concluded that mussels Lévy walk. We confronted a larger model set with these data and found that mussels do not Lévy walk: Their movement is best described by a composite Brownian walk. This shows how model selection based on an impoverished set of candidate models can lead to incorrect inferences.
It is known from many theoretical studies that ecological chaos may have numerous significant impacts on the population and community dynamics. Therefore, identification of the factors potentially enhancing or suppressing chaos is a challenging problem. In this paper, we show that chaos can be enhanced by the Allee effect. More specifically, we show by(More)
Invasion of an exotic species initiated by its local introduction is considered subject to predator-prey interactions and the Allee effect when the prey growth becomes negative for small values of the prey density. Mathematically, the system dynamics is described by two nonlinear diffusion-reaction equations in two spatial dimensions. Regimes of invasion(More)
Spatiotemporal dynamics of a predator-prey system is considered under the assumption that prey growth is damped by the strong Allee effect. Mathematically, the model consists of two coupled diffusion-reaction equations. The initial conditions are described by functions of finite support which corresponds to invasion of exotic species. By means of extensive(More)
Dispersal has long been recognized as a crucial factor affecting population dynamics. Several studies on long-distance dispersal revealed a peculiarity now widely known as a problem of "fat tail": instead of the rate of decay in the population density over large distances being described by a normal distribution, which is apparently predicted by the(More)
A few spatiotemporal models of population dynamics are considered in relation to biological invasion and biological control. The patterns of spread in one and two spatial dimensions are studied by means of extensive numerical simulations. We show that, in the case that population multiplication is damped by the strong Allee effect (when the population(More)
We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the(More)
It has long been recognized that numerical modelling and computer simulations can be used as a powerful research tool to understand, and sometimes to predict, the tendencies and peculiarities in the dynamics of populations and ecosystems. It has been, however, much less appreciated that the context of modelling and simulations in ecology is essentially(More)