Analytic Solutions to a Family of Lotka-Volterra Related Differential Equations
نویسنده
چکیده
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 transformation which allows these systems to be reduced to Hamiltonian form is provided.
منابع مشابه
Analytic Solutions to a Class of Two-dimensional Lotka-volterra Dynamical Systems
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)...
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 کاملThe Lotka-Volterra Predator-Prey Equations
One may find out the application of mathematics in the areas of ecology, biology, environmental sciences etc. Mathematics is particulary used in the problem of predator-prey known as lotka-Volterra predator-prey equations. Indeed, differential equations is employed very much in many areas of other sciences. However, most of natural problems involve some unknown functions...
متن کاملPositive periodic solutions of Lotka-Volterra-like impulsive functional differential equations with infinite distributed time delays on time scales
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...
متن کاملThe Stability of Some Systems of Harvested Lotka-Volterra Predator-Prey Equations
Some scientists are interesting to study in area of harvested ecological modelling. The harvested population dynamics is more realistic than other ecological models. In the present paper, some of the Lotka-Volterra predator-prey models have been considered. In the said models, existing species are harvested by constant or variable growth rates. The behavior of their solutions has been analyzed ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999