Modified Chebyshev Collocation Method For A Delayed Predator-prey System

The mathematical models of population dynamics have attracted much attention due to their theoretical and practical significance.The system of predator-prey interaction is the basic structure in population dynamics.The models in which two species having a predator-prey correlation are present in the environment have taken as the primary point of this work.Based on that,our attention focus on a competitive Lotka Volterra with delay.In the beginning,some elementary formulae for manipulating Chebyshev polynomials and summarizing the critical properties of Chebyshev polynomial have demonstrated.The essential properties of the Chebyshev polynomial are displayed.Areas of the application are introduced and discussed in the chapters devoted to them.Since trigonometric functions are involved,there are many cases in which the discrete orthogonality can be held precisely.In general,of course,the result is only approximately accurate.The approximate solutions of the Lotka-Volterra with delay have been obtained using the Chebyshev collocation method.The essential technique is that this method transforms the primary problem into a system of nonlinear algebraic equations.By using the residual function of the operator equations,error differential equations are formulated.And thus,approximate results are improved.A numerical example is given to realize the method's reliability and applicability,and comparisons with existing results are presented.The numerical results reveal that the obtained solutions are in good agreement with earlier studies.