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Independent control of oscillation frequency and amplitude in HIV–immune dynamics

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  • Zhong, Xing
  • Yang, Zhichun
  • Huang, Tingwen
  • Wang, Conghua

Abstract

HIV–immune interaction models can exhibit sustained oscillations, where frequency sets the cycle time scale and amplitude sets fluctuation size. Because nonlinear coupling typically links frequency and amplitude, changing one often perturbs the other, making locally decoupled modulation nontrivial. Near a Hopf bifurcation, we derive leading-order approximations for the base frequency and saturation amplitude via center-manifold and normal-form analysis, and identify conditions for local decoupling. Building on a phase–amplitude description, we design a nonlinear-only feedback law for independent amplitude modulation that leaves the Jacobian unchanged, and a cascaded linear–nonlinear strategy for independent frequency modulation, where linear feedback assigns a target base frequency and nonlinear compensation restores the desired amplitude. Simulations confirm frequency (amplitude) tuning with small cross-effects on amplitude (frequency) in a Hopf neighborhood. These results clarify model-dependent requirements for local frequency–amplitude decoupling in oscillatory HIV–immune dynamics.

Suggested Citation

  • Zhong, Xing & Yang, Zhichun & Huang, Tingwen & Wang, Conghua, 2026. "Independent control of oscillation frequency and amplitude in HIV–immune dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 208(P1).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p1:s0960077926002870
    DOI: 10.1016/j.chaos.2026.118146
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