Author:
Zhang Zizhen,Wei Ruibin,Xia Wanjun
Abstract
AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference37 articles.
1. World Health Organization report on the global tobacco epidemic (2019). https://apps.who.int/iris/bitstream/handle/10665/326043/9789241516204-eng.pdf
2. Sun, C.X., Jia, J.W.: Optimal control of a delayed smoking model with immigration. J. Biol. Dyn. 13, 447–460 (2019)
3. Khan, S.A., Shah, K., Zaman, G., Jarad, F.: Existence theory and numerical solutions to smoking model under Caputo–Fabrizio fractional derivative. Chaos 29, Article ID 013128 (2019). https://doi.org/10.1063/1.5079644
4. Rahman, G., Agarwal, R.P., Din, Q.: Mathematical analysis of giving up smoking model via harmonic mean type incidence rate. Appl. Math. Comput. 354, 128–148 (2019)
5. Garsow, C.C., Salivia, G.J., Herrera, A.R.: Mathematical models for dynamics of tobacco use, recovery and relapse. Technical report BU-1505-M, Cornell University, Ithaca, NY (2000)
Cited by
19 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献