Abstract

A synthetic drug transmission model with psychological addicts and time delay is proposed in this paper. By analyzing the corresponding characteristic equation and choosing the time delay as the bifurcation parameter, a set of sufficient criteria guaranteeing local stability of the synthetic drug addiction equilibrium and the appearance of a Hopf bifurcation of the model is established. Further, the direction and stability of the Hopf bifurcation are investigated with the aid of normal form theory and center manifold theory. Finally, numerical simulations are performed to support the analytical results.

中文翻译：

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时延对心理成瘾者合成毒品传播模型分叉的影响

摘要

提出了一种具有心理上瘾者和时间延迟的合成药物传递模型。通过分析相应的特征方程并选择时延作为分叉参数，建立了一组保证合成药物成瘾平衡的局部稳定性和模型的Hopf分叉出现的充分判据。此外，借助于法线形式理论和中心流形理论研究了霍夫夫分支的方向和稳定性。最后，进行数值模拟以支持分析结果。