Analytic Solutions to a Class of Two-dimensional Lotka-volterra Dynamical Systems
نویسندگان
چکیده
A novel coordinate transformation is used to reduce a simple generalization of the Lotka-Volterra dynamical system to a single second-order autonomous ordinary differential equation. Formal analytic solutions to this differential equation are presented which are shown to reduce to the recently obtained solution to the LotkaVolterra system [C. M. Evans and G. L. Findley, J. Math. Chem. 25 (1999) 105–110]. An initial analysis of the analytic solution to this latter system results in the specification of a new family of Lotka-Volterra related differential equations.
منابع مشابه
Analytic Solutions to a Family of Lotka-Volterra Related Differential Equations
An initial formal analysis of the analytic solution [C. M. Evans and G. L. Findley, J. Math. Chem., in press] to the Lotka-Volterra dynamical system is presented. A family of first-order autonomous ordinary differential equations related to the LV system is derived, and the analytic solutions to these systems are given. Invariants for the latter systems are introduced, and a simple transformati...
متن کاملAnalytic Solutions to the Lotka-volterra Model for Sustained Chemical Oscillations
The Lotka-Volterra (LV) model of oscillating chemical reactions, characterized by the rate equations has been an active area of research since it was originally posed in the 1920s. In this Review, we present a simple transformation which reduces the two-dimensional LV system to a one-dimensional system modeled by a second-order nonlinear autonomous ordinary differential equation. The formal ana...
متن کاملThree-dimensional discrete-time Lotka–Volterra models with an application to industrial clusters
We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka–Volterra prey–predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka–V...
متن کاملExistence of traveling wave solutions in m-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction
This paper deals with the existence of traveling wave solutions for m-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction. By using Schauder’s fixed point theorem and a cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained will be applied to...
متن کاملDynamical behaviour of Lotka-Volterra systems
We consider the (n 1)-dimensional Lotka-Volterra system (arising in biological modelling of species interactions), and associate with it a family of n-dimensional systems having the same phase portrait. We obtain some results on global behaviour and convergence towards the equilibrium in the case where the LV system is “nearly symmetric” or “nearly cooperative” (that is, there exists a member o...
متن کامل