Influence of time delay on bifurcation of a synthetic drug transmission model with psychological addicts
- Resource Type
- article
- Authors
- Zizhen Zhang; Fangfang Yang; Wanjun Xia
- Source
- Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-15 (2020)
- Subject
- Delay
Hopf bifurcation
Synthetic drugs model
Stability
Periodic solution
Mathematics
QA1-939
- Language
- English
- ISSN
- 1687-1847
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.