2023/08/11 by Javier del Pino, del Pino, Javier, Jan Košata +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Insect and Arachnid Ecology and Behavior #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Dynamics and Pattern Formation #Plant Reproductive Biology #Quantum Gases (cond-mat.quant-gas)
paper · pdf · doi:10.48550/arxiv.2308.06092
openalex publication_date 2023/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz. Correspondingly, their study commonly relies on brute-force time-evolution or on circumstantial evidence such as instabilities of fixed points. Alas, such approaches are unable to account for the coexistence of multiple solutions, as they rely on specific initial conditions. Here, we develop a multifrequency rotating ansatz with which we find limit cycles as stationary states. We demonstrate our approach and its performance in the simplest case of the Van der Pol oscillator. Moving beyond the simplest example, we show that our method can capture the coexistence of all fixed-point attractors and limit cycles in a modified nonlinear Van der Pol oscillator. Our results facilitate the systematic mapping of out-of-equilibrium phase diagrams, with implications across all fields of natural science.