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Research questionHow can periodic orbits in dynamical systems be continued and bifurcations detected without time integration or hand-derived Jacobians?Periodic-orbit continuation requires finding entire families of solutions while tracking changes in their structure. Time integration and manually derived Jacobians can make this search costly and difficult to generalize, especially near unstable solutions and bifurcations.
Research Paper
Latest papersRecent research connected to this question, newest first.Variational Continuation for Double Pendulum Periodic OrbitsThe source demonstrates this problem on periodic double-pendulum oscillations, representing candidate loops with Fourier series and using automatic differentiation to analyze the loss landscape. Reported findings include continuations from fixed points, orbit-family intersections, subharmonic bifurcations, and previously unreported branches; broader applicability is not established by the supplied evidence.research paper · Sep 4, 2026
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