Hopf bifurcation and global exponential stability of an epidemiological smoking model with time delay

In this study, the stability and bifurcation problems of a fractional food chain system with two kinds of delays are studied. Firstly, the nonnegative, bounded, and unique properties of the solutions of the system are proved. The asymptotic stability of the equilibrium points of the system is discussed. Furthermore, the global asymptotic stability of the positive equilibrium point is deduced by using Lyapunov function method. Secondly, the system takes two kinds of time delays as bifurcation parameters and calculates the critical values of Hopf bifurcation accurately. The results show that Hopf bifurcation can advance with increasing fractional order and another delay. In conclusion, numerical simulation verifies and illustrates the theoretical results.

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Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays

Zhang

Zeb

Wan

et al. 2022

Mathematics

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Synthetic drugs are taking the place of traditional drugs and have made headlines giving rise to serious social issues in many countries. In this work, a synthetic drug transmission model incorporating psychological addicts with two time delays is being developed. Local stability and exhibition of Hopf bifurcation are established analytically and numerically by taking the combinations of the two time delays as bifurcation parameters. The exhibition of Hopf bifurcation shows that it is burdensome to eradicate the synthetic drugs transmission in the population.

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Hopf bifurcation and global exponential stability of an epidemiological smoking model with time delay

Cited by 4 publications

References 14 publications

Relaxed positivity, η-exponential stabilization and l1-gain performance of polynomial discrete-time fuzzy system with time-delay and external disturbance

Relaxed positivity, η-exponential stabilization and l1-gain performance of polynomial discrete-time fuzzy system with time-delay and external disturbance

Stability and Bifurcation Analysis of a Fractional‐Order Food Chain Model with Two Time Delays

Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays

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