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Displaying similar documents to “From fast to slow processes in the evolution of urban and regional settlement structures.”

Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

Iwona Karcz-Dulęba (2004)

International Journal of Applied Mathematics and Computer Science

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A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters...

Time to the convergence of evolution in the space of population states

Iwona Karcz-Dulęba (2004)

International Journal of Applied Mathematics and Computer Science

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Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard...

The impatience mechanism as a diversity maintaining and saddle crossing strategy

Iwona Karcz-Duleba (2016)

International Journal of Applied Mathematics and Computer Science

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The impatience mechanism diversifies the population and facilitates escaping from a local optima trap by modifying fitness values of poorly adapted individuals. In this paper, two versions of the impatience mechanism coupled with a phenotypic model of evolution are studied. A population subordinated to a basic version of the impatience mechanism polarizes itself and evolves as a dipole centered around an averaged individual. In the modified version, the impatience mechanism is supplied...