A new numerical approach method to solve the Lotka–Volterra predator–prey models with discrete delays

Jilong He, Zhoushun Zheng and Zhijian Ye

Physica A: Statistical Mechanics and its Applications, 2024, vol. 635, issue C

Abstract: This paper proposes a new approach called Extreme Learning Machine (ELM) to solve the Lotka–Volterra predator–prey models using a novel approximation form. Unlike the traditional methods that involve constructing complex algebraic systems and performing inverse matrix operations, ELM transforms the system of differential equations into a set of nonlinear equations and solves for the parameters through optimization iterations to obtain an approximate solution. Furthermore, we construct a solution form that satisfies the initial conditions, eliminating the need to handle initial conditions during the solving process, making this method more concise. Finally, by comparing with other numerical methods using two sets of models and parameters, ELM can produce high-precision results and further demonstrate the advantages of our method.

Keywords: Extreme Learning Machine; Predator–prey models; System of nonlinear differential equations; Trial function; Iterative optimization; Numerical simulation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:635:y:2024:i:c:s0378437124000323

DOI: 10.1016/j.physa.2024.129524

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