<p>This paper investigates the chaotic dynamics of a resistively and capacitively shunted junction (RCSJ) coupled to a resonant cavity (RLC) through a diode and a multi-periodic pulse source operating at the same frequency as the excitation current. The diode is connected in series with the RCSJ-based Josephson junction, which includes a nonlinear parameter, and the entire system is coupled to a multi-periodic pulse source in series with a resonant cavity containing a coil with internal resistance. The Josephson junction is modeled with a non-sinusoidal current-phase relation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$Ij=I_{0}(sin(\phi )-\alpha .sin2(\phi ))$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>I</mi> <mi>j</mi> <mo>=</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mi>α</mi> <mo>.</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mrow> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where the second harmonic term represents the effects of high-transparency barriers or unconventional Cooper-pairing mechanisms. This formulation makes it possible to analyze chaotic regimes arising from the interaction between the two harmonic components. The governing equations of the model are derived from Kirchhoff’s laws, and the equilibrium points are identified and analyzed both analytically and numerically. The bifurcation behavior and the transition to chaos are examined using the fourth-order Runge–Kutta method, showing that the system exhibits both dc and ac Josephson regimes depending on the excitation frequency and the junction’s phase difference. It is observed that the system dissipates energy, and the chaotic oscillations become more regular at higher values of the coil’s internal resistance. These results indicate that energy losses can be compensated by the multi-periodic pulse source, whose role is to enhance the chaotic oscillations of the excitation current and offset the dissipation caused by the ohmic conductor and the coil’s internal resistance. Finally, the diode serves to attenuate certain hidden orders of the system, which include an infinite number of unstable periodic states. All these objectives are achieved through a comprehensive analysis of the proposed circuit, further supported by an experimental implementation on a microcontroller platform, which validates the numerical simulations.</p>

Chaotic dynamics of a Josephson junction coupled to a resonant cavity controlled by a diode and a multi-periodic pulse source

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发表日期：

2026年2月20日

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M. A. Kakpo,
V. Kamdoum Tamba,
C. H. Miwadinou,
A. V. Monwanou

摘要

This paper investigates the chaotic dynamics of a resistively and capacitively shunted junction (RCSJ) coupled to a resonant cavity (RLC) through a diode and a multi-periodic pulse source operating at the same frequency as the excitation current. The diode is connected in series with the RCSJ-based Josephson junction, which includes a nonlinear parameter, and the entire system is coupled to a multi-periodic pulse source in series with a resonant cavity containing a coil with internal resistance. The Josephson junction is modeled with a non-sinusoidal current-phase relation $Ij=I_{0}(sin(\phi )-\alpha .sin2(\phi ))$ $I j = I_{0} (s i n (ϕ) - α . s i n 2 (ϕ))$ , where the second harmonic term represents the effects of high-transparency barriers or unconventional Cooper-pairing mechanisms. This formulation makes it possible to analyze chaotic regimes arising from the interaction between the two harmonic components. The governing equations of the model are derived from Kirchhoff’s laws, and the equilibrium points are identified and analyzed both analytically and numerically. The bifurcation behavior and the transition to chaos are examined using the fourth-order Runge–Kutta method, showing that the system exhibits both dc and ac Josephson regimes depending on the excitation frequency and the junction’s phase difference. It is observed that the system dissipates energy, and the chaotic oscillations become more regular at higher values of the coil’s internal resistance. These results indicate that energy losses can be compensated by the multi-periodic pulse source, whose role is to enhance the chaotic oscillations of the excitation current and offset the dissipation caused by the ohmic conductor and the coil’s internal resistance. Finally, the diode serves to attenuate certain hidden orders of the system, which include an infinite number of unstable periodic states. All these objectives are achieved through a comprehensive analysis of the proposed circuit, further supported by an experimental implementation on a microcontroller platform, which validates the numerical simulations.