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Bifurcation Analysis and Chaos Control in a Discrete Fractional-Order Model of Immune Response to Abnormal Cells
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DOI：10.17576/jsm-2026-5503-13.png)
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Abstract
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This study investigates the complex dynamics and control of a discrete-time fractional-order model describing the immune response to abnormal cells. We establish the local asymptotic stability of the equilibrium points and derive the specific parametric conditions governing the emergence of Neimark-Sacker and flip bifurcations. Numerical simulations not only confirm these bifurcations but also show the subsequent onset of chaos. To mitigate this, we successfully implement and demonstrate the efficacy of three control strategies state feedback, pole placement, and hybrid control in stabilizing the chaotic regimes and suppressing undesirable bifurcations. The numerical results provide strong validation of the theoretical analysis, underscoring the value of these control techniques for managing pathological dynamics in immune system models.
Keywords:
Discrete immune system model with fractional-order
flip bifurcation
Hopf bifurcation
N-S bifurcation
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113
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