Search results for "time average"

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Models of the population playing the Rock-Paper-Scissors game

2018

We consider discrete dynamical systems coming from the models of evolution of populations playing rock - paper - scissors game . Asymptotic behaviour of trajectories of these systems is described, occurrence of the Neimark-Sacker bifurcation and nonexistence of time averages are proved.

education.field_of_studyGame mechanicsAsymptotic behaviour of trajectoriesDynamical systems theoryComputer scienceApplied Mathematics010102 general mathematicsPopulation01 natural sciences010101 applied mathematicstime averageDiscrete Mathematics and CombinatoricsApplied mathematicsTime averagerock-paper-scissors game0101 mathematicseducationVideo game designBifurcationDiscrete and Continuous Dynamical Systems-Series B
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Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime

1996

We study a dynamical model for an ecological network of many interacting species. We consider a Malthus-Verhulst type of self-regulation mechanism. In the framework of the mean field theory we study the nonlinear relaxation in three different cases: (a) towards the equilibrium state, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations. \textcopyright{} 1996 The American Physical So…

symbols.namesakeNonlinear systemMean field theoryThermodynamic equilibriumCritical point (thermodynamics)GaussiansymbolsTime averageStatistical physicsInstabilityEcological networkMathematics
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