Numerical oscillation of nonlinear generalized delay single species population model

[摘要] In this paper, we mainly consider the oscillation of numerical solutions for a nonlinear delay differential equation which is generalized from a delay Lotka-Volterra type single species population growth model. By studying the corresponding difference scheme of the equation discretized by $\theta$-method, forward Euler method and backward Euler method, some sufficient conditions under which the numerical solutions oscillate are obtained. Furthermore, we prove that the positive non-oscillatory numerical solutions tend to the equilibrium of the original differential equation. Finally, some numerical experiments are given to verify the theoretical results.

[学科分类] 数学（综合）

[关键词] nonlinear differential equation;delay differential equation;θ-method;forward Euler method;backward Euler method;oscillation