Time fluctuations in a population model of adaptive dynamics

Time fluctuations in a population model of adaptive dynamics

We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results about the evolution of populations in environments with time oscillations, the development of concentrations in the form of Dirac masses, the location of the do...

Dynamics of a discrete-time plant-herbivore model

dynamics and bifurcations of a lotka-volterra population model

this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

Fluctuations and dispersal rates in population dynamics.

Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment [J. Dockery, V. Hutson, K. Mischaikow, and M. Pernarowski, J. Math. Biol. 37, 61 (1998)] of two species which differ only in their dispersal rates the slow species always d...

A MODEL FOR EVOLUTIONARY DYNAMICS OF WORDS IN A LANGUAGE

Human language, over its evolutionary history, has emerged as one of the fundamental defining characteristic of the modern man. However, this milestone evolutionary process through natural selection has not left any ’linguistic fossils’ that may enable us to trace back the actual course of development of language and its establishment in human societies. Lacking analytical tools to fathom the cr...