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A delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response
- Source :
- AIMS Mathematics, Vol 6, Iss 1, Pp 1-22 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- This paper gropes the stability and Hopf bifurcation of a delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response. The critical point at which a Hopf bifurcation occurs can be figured out by using the escalating time delay of psychologically addicts as a bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are explored with aid of the central manifold theorem and normal form theory. Specially, global stability of the model is proved by constructing a suitable Lyapunov function. To underline effectiveness of the obtained results and analyze influence of some influential parameters on dynamics of the model, some numerical simulations are ultimately addressed.
- Subjects :
- Lyapunov function
Hopf bifurcation
delay
General Mathematics
Addiction
media_common.quotation_subject
lcsh:Mathematics
Functional response
periodic solution
stability
lcsh:QA1-939
Two stages
Critical point (mathematics)
Synthetic drugs
symbols.namesake
symbols
Applied mathematics
synthetic drugs model
hopf bifurcation
Bifurcation
media_common
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....021bc7b4500fc09c8d5b6cc5f2059774