Chaotic predation scheme for age-clustered one predator–one prey Lotka–Volterra

Abstract

Lotka–Volterra differential equations deal with modeling of predator and prey populations and interrelation of population sizes in a continuous domain. Since all populations, be they predators or prays, are only the estimates in consequence of sampling process, this paper initially concerns with discretization schemes of one predator–prey Lotka–Volterra systems. Second-order Runge–Kutta approximation is used to discretize the original differential equations for flexibility to manipulate the system parameters. Subsequent to discretization, a novel predation scheme is introduced to enhance the rationalization of original model with age cluster-based and detailed rules which are based on reproductivity, predation ability, predation essentiality, food provision and consumption. Aging is also simulated with transitive structure of the algorithms that the alive individuals are getting older and changing clusters after the predation scheme is operated. Experiments revealed that our model exhibits not only fluctuations like the original model but also stable trajectories and fractal structure depending on the model parameters. Therefore, the main novelty of this paper briefly is the discovery of chaotic one predator–one prey system exhibiting chaotic behavior for a narrow interval and revealing a strange attractor which is very unique.