Abstract
In this work, a principle for getting heteroclinic orbit of a dynamical system has been proposed when the solution is known in a compact form. The proposed principle has been tested through its application to a three species Lotka-Volterra system, which may appear as a mathematical model of human pathogen system. The domain in parameter space involve in the model, and the region of initial condition for the existence of heteroclinic orbit have been derived.
Highlights
Lotka-Volterra (LV) system is one of the widely used models in the field of nonlinear dynamics
We have derived here explicit time and parameter dependent solution in a compact form of LV system with some parameters which may be used as a mathematical model for human pathogen system
Information available from the exact solutions helped us to propose a principle for the existence of heteroclinic orbit for this system
Summary
Lotka-Volterra (LV) system is one of the widely used models in the field of nonlinear dynamics. Several methods for obtaining invariants for the system of nonlinear ordinary differential equations(ODEs) like LV system [10,11,12,13,14,15,16,17] are available in the literature but getting their solutions in closed form (in terms of elementary known function) even for a simpler system is not an easy task. Getting the analytic expression for heteroclinic orbit between two fixed points is not inevitable Purpose of this brief report is to obtain an exact analytic solution of the system of equations (1) to deriving a condition for the existence and time-dependent solution in a compact form of heteroclinic orbits as well as to find the domain in phase-space where heteroclinic orbit exists.
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