Abstract
The paper deals with the dynamical behavior of a discrete-time ratio-dependent predator–prey system. The predator dependence is one of the main concerns of the system. The stability analysis of this 2-dimensional map was carried out analytically. Numerical simulation was carried out to verify the analytical results. We analyzed some specific features that could arise in discrete system. Basin of attraction was found for the endemic equilibrium state. We extended the numerical simulation for the maximal Lyapunov exponent. The presence of positive Lyapunov exponent indicated chaotic behavior of the map. The sensitive dependence on initial condition is one of the criteria for a discrete system. We showed that the system is sensitive on the initial conditions. We also carried out the analysis of diffusion and impact of noise.
Highlights
The pioneering work of [1,2] on population biology is the threshold created in today’s explosion of the field of population biology
We investigated the stability behavior and different features of a discrete type ratio-dependent predator–prey system
In most predator–prey systems, the predator is to search for food and compete for food, and the more realistic functional response is a function which is dependent on both prey and predator densities
Summary
The pioneering work of [1,2] on population biology is the threshold created in today’s explosion of the field of population biology. The prey dependence [4] trophic interactions in the population model have reigned for long time, even today [5]. If the trophic function depends on the single variable N/P (N, the prey, P, the predator), the essential properties of predator dependence are rendered, called ratio-dependence [4] The work on this ratio-dependence model has mainly focused on continuous models. Danca demonstrated that the discrete-time predator–prey model with Holling type I functional response exhibits a chaotic behavior [6]. The discrete time ratio-dependent predator–prey explains the chaotic dynamics of the model system. We investigated the stability behavior and different features of a discrete type ratio-dependent predator–prey system.
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