Wavefronts in Time-Discrete Space-Continuous Fisher-Kolmogorov Equation
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| Year of publication | 2014 |
| Type | Conference abstract |
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| Description | The Fisher-Kolmogorov reaction-diffusion equation was originally introduced as a model of biological invasions, i.e. of genes or populations advance. This equation admits travelling wave solution and, this way, it opens a problem of determination a speed of the wave and a shape of the wavefront. An important modification of the equation consists in discretisation of time in the reaction term; it describes growth and dispersal of a population with non-overlapping generations. The aim of the contribution is to study the modified equation under some natural hypotheses put on the growth function and on patterns of dispersion. The wavefront shape is extracted as a difference equation solution. |