We study the collapse of Hamiltonian chaos in a four-pendulum system under dissipation, providing a theoretical and numerical framework for understanding how non-conservative forces transform chaotic behavior into stable, predictable dynamics. By analyzing the conservative dynamics, we demonstrate the system’s inherent chaotic properties. The introduction of linear damping leads to analytical proof, via Lyapunov’s method, that the system’s once complex and chaotic phase space collapses to a single globally stable equilibrium. Our findings elucidate how dissipation serves as a powerful mechanism that imposes order on an otherwise chaotic system, offering insights into the broader implications of chaos suppression in nonlinear dynamics.
Reference
[1] Baladron, C., Khrennikov, A. (2023) Simulation of Closed Timelike Curves in a Darwinian Approach to Quantum Mechanics. Universe, 9(2), 64.
[2] Lorenz, E. N. (2017) Deterministic nonperiodic flow 1. In Universality in Chaos, 2nd edition, 367-378.
[3] Golovnev, A. (2023) On the role of constraints and degrees of freedom in the Hamiltonian formalism. Universe, 9(2), 101.
[4] Tomé, T., de Oliveira, M. J. (2022) Stochastic motion in phase space on a surface of constant energy. Physical Review E, 106(3), 034129.
[5] Hixon, R. (2019) Deterministic period mean flow boundary condition for unsteady flow predictions. Computers & Fluids, 190, 337-345..
[6] Thompson, J. M. T. (2025) Chaos Theory. In Colorful Views of Stability and Chaos, 163-208.
[7] Thomas, G. F. (2023) The Arrow of Time and Its Irreversibility. Available at SSRN 4560199.
[8] Takeishi, N., Kawahara, Y. (2021) Learning dynamics models with stable invariant sets. In Proceedings of the AAAI Conference on Artificial Intelligence, 35(11), 9782-9790.
[9] García-Sandoval, J. P., Hudon, N., Dochain, D. (2016) Conservative and dissipative phenomena in thermodynamical systems stability. IFAC-PapersOnLine, 49(24), 28-33.
[10] De Giuli, E. (2025) Noise equals control. Physical Review E, 112(2), 024142.
Share and Cite
Luo, J., He, J. (2025) Dissipation-Induced Order: The Collapse of Hamiltonian Chaos in a Four-Pendulum System. Scientific Research Bulletin, 2(1), 8-21.