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<p>To investigate the neuronal firing dynamics, this study introduces a modified FitzHugh–Nagumo (FHN) circuit integrated with a fractional-order memristor. The system architecture is established through coupling with a diode bridge memristor with bias voltage source, subsequently extended from integer-order model to fractional-order formalism for enhanced biological plausibility. Comprehensive dynamical analysis employing phase plane trajectories, bifurcation topology, and equilibrium point stability was conducted to characterize parameter-dependent behaviors. Numerical verification was implemented via PSpice circuit simulation, with experimental data demonstrating strong alignment with numerical simulation. Hardware validation is further performed using the NI PXIe platform interfaced with LabVIEW, yielding measurement results that closely matched both numerical solutions and circuit simulation. This multi-platform verification framework confirms the theoretical model’s mathematical consistency and engineering realizability. Notably, both the integer-order and fractional-order systems exhibit quasi-periodic bursting oscillations at parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> = −&#xa0;0.5 and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> = −&#xa0;0.4, replicating characteristic neural firing patterns. When the parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> is in the range of −&#xa0;1.3 to −&#xa0;0.1, there is a significant difference in the bifurcation behavior between the integer-order system and the fractional-order system (q = 0.98). The observed transition dynamics between quiescent and active states demonstrate remarkable similarity to in vitro neuronal recordings, suggesting potential applications in neuromorphic computing and neural oscillation modeling.</p>

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Modeling and Dynamic Analysis of a Novel Fractional Order Memristor-Based FitzHugh–Nagumo Circuit with Bias Voltage Source

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Chaojun Wu,
  • Bin Xu,
  • Tongtong Yang,
  • Ningning Yang

摘要

To investigate the neuronal firing dynamics, this study introduces a modified FitzHugh–Nagumo (FHN) circuit integrated with a fractional-order memristor. The system architecture is established through coupling with a diode bridge memristor with bias voltage source, subsequently extended from integer-order model to fractional-order formalism for enhanced biological plausibility. Comprehensive dynamical analysis employing phase plane trajectories, bifurcation topology, and equilibrium point stability was conducted to characterize parameter-dependent behaviors. Numerical verification was implemented via PSpice circuit simulation, with experimental data demonstrating strong alignment with numerical simulation. Hardware validation is further performed using the NI PXIe platform interfaced with LabVIEW, yielding measurement results that closely matched both numerical solutions and circuit simulation. This multi-platform verification framework confirms the theoretical model’s mathematical consistency and engineering realizability. Notably, both the integer-order and fractional-order systems exhibit quasi-periodic bursting oscillations at parameters \(a\)  = − 0.5 and \(a\)  = − 0.4, replicating characteristic neural firing patterns. When the parameter \(a\) is in the range of − 1.3 to − 0.1, there is a significant difference in the bifurcation behavior between the integer-order system and the fractional-order system (q = 0.98). The observed transition dynamics between quiescent and active states demonstrate remarkable similarity to in vitro neuronal recordings, suggesting potential applications in neuromorphic computing and neural oscillation modeling.