NDLI: A method for Lyapunov spectrum estimation using cloned dynamics and its application to the discontinuously-excited FitzHugh

Content Provider	Springer Nature Link
Author	Soria, Diogo C. Fazanaro, Filipe I. Suyama, Ricardo Oliveira, José Raimundo Attux, Romis Madrid, Marconi K.
Copyright Year	2011
Abstract	This work presents a new method to calculate the Lyapunov spectrum of dynamical systems based on the time evolution of initially small disturbed copies (“clones”) of the motion equations. In this approach, it is not necessary to construct the tangent space associated with the time evolution of linearized versions of motion equations, being the Lyapunov exponents directly estimated in terms of the rate of convergence or divergence of these disturbed clones with respect to the fiducial trajectory, there being periodic correction via the Gram–Schmidt Reorthonormalization procedure. The proposed method offers the possibility of partial estimation of the Lyapunov spectrum and can also be applied to nonsmooth dynamics, since the linearization procedure is no longer required. The idea is tested for representative continuous- and discrete-time dynamical systems and validated by means of comparison with the classical method to perform this calculation. To illustrate its applicability in the nonsmooth context, the largest Lyapunov exponent of the FitzHugh–Nagumo neuronal model under discontinuous periodic excitation is calculated taking the amplitude of stimulation as control parameter. This analysis reveals some complex behaviours for this simple neuronal model, which motivates relevant discussions about the possible role of chaos in the cognitive process.
Starting Page	413
Ending Page	424
Page Count	12
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	67
Issue Number	1
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-03-16
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chaos Lyapunov spectrum estimation FitzHugh–Nagumo neuronal model Discontinuous excitation Nonsmooth models Mechanical Engineering Vibration, Dynamical Systems, Control Automotive Engineering Mechanics
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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