A path inside Arnold tongue arising from Neimark–Sacker bifurcation
| Authors | |
|---|---|
| Year of publication | 2026 |
| Type | Article in Periodical |
| Magazine / Source | Communications in Nonlinear Science and Numerical Simulation |
| MU Faculty or unit | |
| Citation | |
| web | https://www.sciencedirect.com/science/article/pii/S1007570425005970 |
| Doi | https://doi.org/10.1016/j.cnsns.2025.109186 |
| Keywords | Arnold tongues; Frequency locking; Singularity theory; Neimark–Sacker bifurcation |
| Description | We have proved that there exists a local polynomial path in the parameter space which passes through the Arnold tongue starting at the point of resonance on the Neimark–Sacker bifurcation curve for ordinary differential equations, and moreover we have shown a way to compute its coefficients. Our procedure is based on Lyapunov–Schmidt reduction and singularity theory and is further evidence that the application of these tools in bifurcation theory can lead to new and useful results. The derived formula can help to develop an algorithm that would automatically continuate Arnold tongues to a given order along the Neimark–Sacker bifurcation curve. |
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