The Generalized Lotka-Volterra (GLV) model: wi(t+ 1) = λwi(t) + aw̄(t)− cw̄(t)wi(t) , i = 1, ......, N provides a general method to simulate, analyze and understand a wide class of phenomena that are characterized by power-law probability distributions: P (w)dw ∼ wdw (α ≥ 1) and truncated Levy flights fluctuations Lα(w̄).

This paper is a review on some recent works on the Liouville integrability of a large class of Lotka-Volterra systems.

Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as space-dependent, so-called Fokker-Planck diffusion. The invader’s diffusion is taken as neutral Fickian. Furthermore, it is studied how multiplicative environmental noise ...

This report introduces the ideas behind particle filters, looking at the Kalman filter and the SIS and SIR filters to learn about the latent state of state space models. It then introduces particle MCMC as a way of learning about the parameters behind these models. Finally, the SIR filter and particle MCMC algorithms are applied to reaction networks, in particular the Lotka Volterra model.

A complete classification for the global dynamics of a Lotka-Volterra two species competition model with seasonal succession is obtained via the stability analysis of equilibria and the theory of monotone dynamical systems. The effects of two death rates in the bad season and the proportion of the good season on the competition outcomes are also discussed.

this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

Human decision-making does not conform to the independent hypothesis from classical theory. Thus, we introduce quantum theory into Lotka–Volterra model (L–V model), investigate player population dynamics while incorporating initial strategy, game payoffs and interactive strategies in an open social system. Simulation results show that: (1) entanglement intensity of strategy interaction, impact ...