Synchronization in a non-autonomous, non-Hamiltonian conservative chaotic system: Detection and phenomenology

Synchronization has been extensively investigated in dissipative systems, whereas its study in conservative systems remains limited due to the absence of attractors and the possible unbounded growth of trajectories. In this work, we analyze the dynamical behavior and synchronization properties of a three-dimensional non-autonomous, non-Hamiltonian conservative chaotic system. The results of the dynamical analysis reveals the presence of quasi-periodic, chaotic, and hyperchaotic regimes. These behaviors are either bounded or divergent trajectories, depending on parameter values and initial conditions. Synchronization is quantified using phase coherence and synchronization error. These measures are computed from velocities (time derivatives) instead of positions (state variables) to avoid the influence of long-term divergence of positions. This is due to the structure of the system equations, where each velocity is expressed through sinusoidal functions, that remain bounded and make them more suitable observables. For two coupled units, the velocity-based measures provide well-defined synchronization regions in the parameter space, corresponding to chaotic dynamics. The synchronization is found to persist even for moderate values of parametric mismatch. For the star network of coupled conservative systems, the analysis reveals a form of remote synchronization under appropriate parameter values. When hierarchical network structures are considered, synchronization propagates across the different levels, leading to global coherence. The effect of parametric mismatch on synchronization is found to be different for different observables. The position-based evaluation reveals the rapid degradation of coherence due to the growth of amplitude differences, while the velocity-based evaluation reveals the gradual degradation. Finally, introducing dissipation confines trajectories to a bounded attractor, allowing synchronization to be directly assessed from the state variables. To the best of authors’ knowledge, this study provides the first systematic analysis of synchronization in such conservative chaotic systems using velocity-based measures and reports a phenomenon analogous to remote synchronization in conservative networks.