文摘
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate periodic or chaotic reference signals. Classical oscillators evolve in the space R⌃n, typically with n=1 (e.g., the van der Pol vacuum-tube-based oscillator), n = 2 (e.g., the FitzHugh–Nagumo model of spiking neurons) or n=3 (e.g., the Lorenz simplified model of turbulence). The current paper presents a general scheme for the numerical implementation and computer-based simulation of a second-order, nonlinear oscillator model on Riemannian manifolds. The current paper also presents several instances of this model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of the symmetric, positive-definite matrices.
