![]() The FPTD and FPTM by taking one of the barriers as absorbing and the other barrier as reflecting. Our results for first passage time densities and FPTM for crossing of the barriers. We also derived the results of Weiss and Szabo model from In our study we use the imbedding method to derive the first passage time densities(FPTD) by imbedding the boundaryĬonditions for crossing the barriers into the master equations. There the boundary conditions for the first passage time moments have been introduced Of master equations, the integral equations for first passage time moments (FPTM) have been transformed exactly into ordinaryĭifferential equations by Weiss and Szabo. We discuss first passage time problems for a class of one dimensional master equations with separable kernels. KeywordsChaotic neural network–Lagrange–Simulated annealing–Optimization–Chaos–Hopfield Furthermore, AL-CSA’s convergence time is shorter and choice of system parameters is easier Of the traveling salesman problem show that AL-CSA can maintain CSA’s good solution quality while avoiding the potential difficultiesĪssociated with penalty terms. Simulation results on two constrained optimization benchmarks derived from the Hopfield–Tank formulation This, we incorporate augmented Lagrange multipliers into CSA, obtaining a method that we call augmented Lagrange chaotic simulatedĪnnealing (AL-CSA). The relative magnitude of the penalty term, so as to achieve a high quality solution which is at the same time valid. ![]() ThereĮxists a conflict between solution quality and solution validity in the penalty approach. CSA uses a penalty term to enforce solution validity as in the original Hopfield–Tank approach. Extinction-persistence transitionsĬhaotic simulated annealing (CSA) proposed by Chen and Aihara has been successfully used to solve a variety of combinatorial Role of Allee effect in enhancing chaos presents an opportunityįor its application in control of biological invasions and conservation of small populations. Of all animals are governed by two basic processes: a) growth and b) dispersal, existence of EOC puts a recent theory of ecologicalĬhaos (Upadhyay, 2009 Rai and Upadhyay, 2006) on robust footing. Is a vital result as existence of EOC has not been demonstrated in a reaction-diffusion system yet. Two dimensional (2D) parameter scan studies reveal that the system dynamics is self-organized at Edges of Chaos (EOC). Dispersal of species is assumed to be a random process in one-dimension only. When community’s local dynamics displays sustained periodic oscillations, the system’s spatio-temporalĭynamics supports periodic traveling waves. The predator-prey community dynamics is assumed We investigate a spatial predator-prey system predator under Allee effect.
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