A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation

Amine, Saïda; Hajri, Youssra; Allali, Karam

doi:10.1016/j.chaos.2022.112396

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…Recently, some articles have focused on the delay-driven Hopf bifurcation of fractionalorder dynamical systems. For example, Amine et al [40] analyzed the stability and Hopf bifurcation of a fractional tumor virotherapy system with delay. Xu et al [41] revealed the impact of both delays on Hopf bifurcation in fractional four-dimensional neural networks.…”

Section: Introductionmentioning

confidence: 99%

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

Zhang,

2024

Fractal Fract

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In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order delay-coupled FitzHugh–Nagumo neural model is acquired. By designing a proper PDp controller, we can efficaciously control the stability domain and the time of emergence of the bifurcation phenomenon of the considered fractional delay-coupled FitzHugh–Nagumo neural model. By exploiting a reasonable hybrid controller, we can successfully adjust the stability domain and the bifurcation onset time of the involved fractional delay-coupled FitzHugh–Nagumo neural model. This study shows that when the delay crosses a critical value, a Hopf bifurcation will arise. When we adjust the control parameter, we can find other critical values to enlarge or narrow the stability domain of the fractional-order delay-coupled FitzHugh–Nagumo neural model. In order to check the correctness of the acquired outcomes of this article, we present some simulation outcomes via Matlab 7.0 software. The obtained theoretical fruits in this article have momentous theoretical significance in running and constructing networks.

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Section: Introductionmentioning

confidence: 99%

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

Zhang,

2024

Fractal Fract

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“…Several recent works give an interesting results as showing that optimal therapy can control proliferation to reduce specially cervical cancer [14], the formulating of a hybrid PDE-ODE Model test the feasibility and well-posedness [15] of the cancer velocity, in a stochastic approach to show colorectal cancer prediction [16], SEIR epidemic model with fractional order [17] estimating mutation rates tumor, and with fractional approach [18], eliminating cancer cells with immune system less, an new model is also studied [19] to present and analysis fractional-order tumor virotherapy model with two time delays. In the same sense, we can note that among the recent models, we find the model named the Normal Tumor Immune UNHealthy Diet Model (NTIUNHDM) [20] that describes well the dynamic of cancer with immunity and proposes the system of ordinary differential equations as follow:…”

Section: Introductionmentioning

confidence: 99%

Fractional derivative model for tumor cells and immune system competition

Elkaf¹,

Allali²

2023

Math. Model. Comput.

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Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing. So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer's evolution under immunity of the body. We will analyze the stability of the formulated system at different equilibrium points. Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer's dynamics.

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Exploring the Impact of Delay on Hopf Bifurcation of a Type of BAM Neural Network Models Concerning Three Nonidentical Delays

Li,

Gao,

et al. 2023

Neural Process Lett

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A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation

Cited by 4 publications

References 25 publications

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

Fractional derivative model for tumor cells and immune system competition

Exploring the Impact of Delay on Hopf Bifurcation of a Type of BAM Neural Network Models Concerning Three Nonidentical Delays

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