Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the syste...

Multi-species Lotka±Volterra models exhibit greater instability with an increase in diversity and/or connectance. These model systems, however, lack the likely behavior that a predator will prey more heavily on some species if other prey species decline in relative abundance. We ®nd that stability does not depend on diversity and/or connectance in multi-species Lotka±Volterra models with this `...

Besides being structurally unstable, the Lotka-Volterra predator-prey model has another shortcoming due to the invalidity of the principle of mass action when the populations are very small. This leads to extremely large populations recovering from unrealistically small ones. The effects of linear modifications to structurally unstable continuous-time predator-prey models in a (small) neighbour...

Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial condition. This characteristics allows us to calculate the effect of periodic seasonal changes on population densities of different species.

In this paper, the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin’s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results. Keywords—Multiple positive periodic solutions; Nonautonomous Lotka-Volterra...

a nonstandard finite difference (nsfd) scheme has been constructed and analyzed for a mathematical model that describes lotka–volterra food web model. this new discrete system has the same stability properties as the continuous model and,on the whole, it preservesthe same local asymptotic stability properties. linearized stability theory and schur–cohn criteria are used for local asymptoticstab...

This paper is concerned with the Lotka-Volterra-like functional differential equations with impulses and infinite distributed time delays on time scales. By applying a fixed point theorem of strict-set contractions, some sufficient conditions have been established to guarantee the existence of periodic solutions. As applications, the existence of positive periodic solutions is given for some co...

Multi-species Lotka-Volterra models exhibit greater instability with an increase in diversity and/or connectance. These model systems, however, lack the likely behavior that a predator will prey more heavily on some species if other prey species decline in relative abundance. We find that stability does not depend on diversity and/or connectance in multi-species Lotka-Volterra models with this ...

By using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results. Keywords—Positive periodic solutions; Lotka-Volterra competition system; Coincidence degree; Harvesting term.