| Abstract: |
| Fractional-order damping provides a compact way to incorporate memory effects into nonlinear dynamical models beyond instantaneous viscous dissipation. In this talk we investigate how introducing a fractional derivative in the dissipative term reshapes both transient evolution and asymptotic dynamics in nonlinear systems, with the fractional order $\alpha$ as a control parameter. Through systematic numerical experiments, we quantify changes in the time required to reach the long-term regime (e.g., convergence to attractors, well-to-well transitions, or escape events) and compare behaviors across parameter ranges that are classically underdamped and overdamped. The results show that memory can qualitatively reorganize the effective damping landscape: regimes that are simple in the integer-order overdamped limit may become structurally richer when $\alpha$ is varied, with altered thresholds and enhanced sensitivity in parameter space. In addition, fractional dissipation can promote resonance-like amplification and frequency-selective responses without modifying the conservative part of the dynamics, providing a new tuning mechanism for nonlinear response. The presented viewpoint is general and can be extended to coupled oscillators and excitable systems. |
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