An Approximate Analytical Algorithm for Solving The Multispecies Lotka-Volterra Equations

In this paper, a new efficient method called the parametric iteration method (PIM) is applied to accurately solve the multispecies Lotka–Volterra equations (MLVEs). Some cases of MLVEs are highlighted in order to show the simplicity and efficiency of the method. The results obtained in this work demonstrate that the present algorithm is a powerful analytic tool for the solution of MLVEs

Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method

The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given

Solving fractional-order competitive lotka-volterra model by nsfd schemes

In this paper, we introduce fractional-order into a model competitive LotkaVolterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard finite difference (NSFD) scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.Publisher's Versio

Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations

Animal movement is a key mechanism for shaping population dynamics. The effect of interactions between competing animals on a population's survival has been studied for many decades. However, interactions also affect an animal's subsequent movement decisions. Despite this, the indirect effect of these decisions on animal survival is much less well-understood. Here, we incorporate movement responses to foreign animals into a model of two competing populations, where inter-specific competition is greater than intra-specific competition. When movement is diffusive, the travelling wave moves from the stronger population to the weaker. However, by incorporating behaviourally induced directed movement towards the stronger population, the weaker one can slow the travelling wave down, even reversing its direction. Hence movement responses can switch the predictions of traditional mechanistic models. Furthermore, when environmental heterogeneity is combined with aggressive movement strategies, it is possible for spatially segregated co-existence to emerge. In this situation, the spatial patterns of the competing populations have the unusual feature that they are slightly out-of-phase with the environmental patterns. Finally, incorporating dynamic movement responses can also enable stable co-existence in a homogeneous environment, giving a new mechanism for spatially segregated co-existence