An inductively coupled system composed of two identical linear resistive-capacitive shunted Josephson junction (LRCSJJ) circuits driven by external direct current (DC) sources was modeled and analyzed in this study. The coupling between the junctions was realized through a shared inductor. The existence and nature of equilibrium states were shown to depend critically on the normalized DC bias currents applied to the junctions. It was demonstrated that the coupled LRCSJJ system admits either an unique equilibrium point or no equilibrium points at all, depending on the biasing conditions. A comprehensive linear stability analysis of the equilibrium point was carried out, revealing that its stability is jointly governed by the inductive coupling strength and the magnitude of the normalized DC currents. When a single stable equilibrium point exists, the system operates in an excitable regime. Conversely, when equilibrium points are absent, sustained oscillatory dynamics emerge. The analysis highlights the role of inductive coupling in regulating the balance between dissipation, energy storage, and nonlinear Josephson dynamics, thereby shaping the global behavior of the coupled system. These results provide fundamental insight into the controllable dynamical regimes of inductively coupled Josephson junction (JJ) circuits and may be of relevance for the design of superconducting electronic devices, including neuromorphic circuits and high-frequency oscillators, where excitability and oscillation play a functional role.
Nonlinear dynamical systems operating under explicit constraints may exhibit qualitatively different closed-loop behaviours depending on the interaction between system coupling, feasibility boundaries, and feedback decision mechanisms. In constrained optimization-based control frameworks, such behaviour often manifests as distinct operating regimes and regime transitions that cannot be captured through local linear analysis. This study investigates constraint-induced nonlinear operating regimes arising in nonlinear model predictive control by considering quadrotor trajectory tracking as a representative constrained intelligent dynamical system. A physics-based rigid-body Newton–Euler model is embedded within a receding-horizon optimization framework with explicit actuator saturation and attitude safety constraints. Beyond conventional tracking objectives, the analysis adopts a system-level perspective to examine how nonlinear translational–rotational coupling and constraint activation jointly shape the qualitative structure of the closed-loop response. Comparative numerical simulations are conducted for both mild and aggressive reference maneuvers under varying constraint boundaries. The resulting responses reveal two dominant classes of nonlinear behaviour: constraint-inactive regimes, in which coupling-driven dynamics govern convergence characteristics, and constraint-active regimes, in which feasibility limits reallocate control authority and dominate transient response. Increased maneuver aggressiveness amplifies coupling-dominated effects, whereas tightened constraints induce regime transitions characterised by feasibility-driven dynamics. The results demonstrate that nonlinear model predictive control functions not only as an effective control strategy for constrained trajectory tracking, but also as a structured analytical tool for characterising regime-dependent behaviour in nonlinear intelligent systems. The findings provide insight into performance limitations, stability-relevant behaviour, and design trade-offs arising from the interplay between nonlinear dynamics and constraint geometry.
Open Access
Journal Metrics
Journal Overview
Associated Journals