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Chapter 16
An Optimization Approach for Finding
a Spectrum of Lyapunov Exponents
Panos M. Pardalos, Vitaliy A. Yatsenko, Alexandre Messo, Altannar Chinchuluun,
and Petros Xanthopoulos
Abstract In this chapter, we consider an optimization technique for estimating the
Lyapunov exponents from nonlinear chaotic systems. We then describe an algo-
rithm for solving the optimization model and discuss the computational aspects of
the proposed algorithm. To show the efficiency of the algorithm, we apply it to some
well-known data sets. Numerical tests show that the algorithm is robust and quite ef-
fective, and its performance is comparable with that of other well-known algorithms.
16.1 Introduction
Brain electrical activity can be recorded from electrodes placed on the scalp or intra-
cranial. It is now possible to record from relatively large areas with macro-electrodes
(EEG) or from more localized regions, using microelectrodes. Such recordings, per-
formed in awake, moving animals, and humans have advanced our understanding of
 
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