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In this paper, we are interested in an integro-differential model that describe the evolution of a population structured with respect to a continuous trait. Under some assumption, we are able to find an entropy for the system, and show that some steady solutions are globally stable. The stability conditions we find are coherent with those of Adaptive(More)
We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed c * > 0, and prove the existence(More)
We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed c * > 0, and prove the(More)
We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin. For locally attractive singular interaction(More)
We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in [8] and [2] to prove the convergence to a unique stable equilibrium. Résumé. Nousétudions un système généralisé d'´ equations différentielles modélisant un nombre fini de populations biologiques en interaction(More)
We study sexual populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. Departing from an infinitesimal model, we perform an asymptotic limit to derive the system introduced in Kirkpatrick and Barton (1997). We then perform a further simplification to obtain a simple model. Thanks to this simpler equation, we can(More)
We study sexual populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. Departing from a structured population equation we perform a hydrodynamic-type limit to derive a model close to an existing model of theoretical biology. We then perform a further simplification to obtain a model depending on only one(More)