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Modelling and Mathematical Analysis of the Glass Eel Migration in the Adour River Estuary

M. Odunlami, G. Vallet (2012)

Mathematical Modelling of Natural Phenomena

In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.

Modelling the spiders ballooning effect on the vineyard ecology

E. Venturino, M. Isaia, F. Bona, E. Issoglio, V. Triolo, G. Badino (2010)

Mathematical Modelling of Natural Phenomena

We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.

Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion

Kousuke Kuto, Yoshio Yamada (2004)

Banach Center Publications

This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case. Our...

New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model

Bingwen Liu (2015)

Annales Polonici Mathematici

This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays, which is defined on the nonnegative function space. Under appropriate conditions, we establish some criteria to ensure that all solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give an example with numerical simulations to illustrate our main results.

Non local reaction-diffusion equations modelling predator-prey coevolution.

Angel Calsina, Carles Perelló, Joan Saldaña (1994)

Publicacions Matemàtiques

In this paper we examine a predator-prey system with a characteristic of the predator subject to mutation. The ultimate equilibrium of the system is found by Maynard-Smith et al. by the so-called ESS (Evolutionary Stable Strategy). Using a system of reaction-diffusion equations with non local terms, we conclude that ESS result for the diffusion coefficient tending to zero, without resorting to any optimization criterion.

Nonlinear evolution equations with exponential nonlinearities: conditional symmetries and exact solutions

Roman Cherniha, Oleksii Pliukhin (2011)

Banach Center Publications

New Q-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet conditions...

Currently displaying 241 – 260 of 449