Study of type-III intermittency in the Landau–Lifshitz-Gilbert equation

Abstract

We have studied a route of chaos in the dissipative Landau-Lifshitz-Gilbert equation representing the magnetization dynamics of an anisotropic nanoparticle subjected to a time-variant magnetic field. This equation presents interesting chaotic dynamics. In the parameter space, for some forcing frequency and magnetic strength of the applied field, one observes a transition from a regular periodic behavior to chaotic dynamics. The chaotic dynamics, close to the bifurcation, are characterized by type-III intermittency. Long epochs of quasi-regular dynamics followed by turbulent bursts. The characterization of the intermittencies has been done through four different techniques. The first method is associated with the computation of the Lyapunov exponents that characterize the chaotic regime. The second and third methods are associated with the statistics of the duration of the laminar epochs prior to a turbulent burst. The fourth method is associated with the subharmonic instability present in those laminar epochs and quantified through a Poincaré section method. At the end of the manuscript, we compare the result obtained by the different techniques and discuss the methods' limitations. RECEIVED

Chaotic intermittency with non-differentiable M(x) function

“…Each reinjection process verifies a linear M (x) function (see equation ( 2)). We call M a (x) and M b (x) these functions for each reinjection process, and they verify the equation (10), (10) where xa and xb are the lower boundary of reinjection for the reinjection processes a and b respectively. From equation ( 10) and using the theory described in Section 2, we get two independent RPD functions as expressed in equation (11),…”

“…The laminar or regular phases are pseudo-equilibrium or pseudo-periodic solutions, while the bursts correspond to chaotic evolution [1][2][3]. The phenomenon of chaotic intermittency has been found in different fields of science as physics, chemistry, medicine, engineering, and economics [4][5][6][7][8][9][10][11][12][13][14][15][16]. Therefore, a better description and understanding of the chaotic intermittency phenomenon would contribute to several fields of knowledge.…”