Two-Sex Branching Interacting Particle Systems and Related Limit Equation
We construct a two-sex branching interacting particle systems as the solutions of jump-type stochastic integral equations,in which a particle can mate with a heterosexual particle randomly.The number of their offspring is a random variable determined by a generating function which is depends on the particles'traits and the current system.We prove that under appropriate conditions,the renormalization of this branching interacting particle system converges to a measure valued function which satisfies a specific nonlinear ordinary differential equation.Finally,we obtain a nonlinear ordi-nary differential equation system to describe the distribution of the traits of the two subpopulation.
two-sex branching interacting particle systemsstochastic integral equationscaling limitmeasure-value function
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