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<p>In this study, a fractional-order formulation of the Stepanova tumor-immune model is developed to explore complex tumor dynamics. To address the limitations of continuous time systems in capturing chaotic behavior in low dimensional settings, the model is transformed into a discrete time structure via piecewise constant arguments. The resulting system admits biologically meaningful equilibrium states, and their local stability is examined. Variations in the tumor carrying capacity parameter lead to a Neimark-Sacker bifurcation, generating quasi-periodic oscillations and, for larger values, chaos, as confirmed by Lyapunov exponent analysis. To mitigate these irregular behaviors, a feedback control mechanism incorporating chemotherapy and immunotherapy effects is proposed. Numerical simulations show that the control strategy effectively suppresses chaos and drives the system toward a tumor dormant state. The proposed framework offers a useful tool for analyzing and regulating complex tumor dynamics.</p>

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Existence of chaos and its control in a fractional order Stepanova tumor model under chemotherapy and immunotherapy effects with piecewise constant arguments

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Neriman Kartal

摘要

In this study, a fractional-order formulation of the Stepanova tumor-immune model is developed to explore complex tumor dynamics. To address the limitations of continuous time systems in capturing chaotic behavior in low dimensional settings, the model is transformed into a discrete time structure via piecewise constant arguments. The resulting system admits biologically meaningful equilibrium states, and their local stability is examined. Variations in the tumor carrying capacity parameter lead to a Neimark-Sacker bifurcation, generating quasi-periodic oscillations and, for larger values, chaos, as confirmed by Lyapunov exponent analysis. To mitigate these irregular behaviors, a feedback control mechanism incorporating chemotherapy and immunotherapy effects is proposed. Numerical simulations show that the control strategy effectively suppresses chaos and drives the system toward a tumor dormant state. The proposed framework offers a useful tool for analyzing and regulating complex tumor dynamics.