The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?

Jay Prakash Singh and B.K. Roy

Chaos, Solitons & Fractals, 2016, vol. 92, issue C, 73-85

Abstract: This review paper aims at answering a basic question on the sign of Lyapunov exponents. A few recent papers reported hyperchaotic system having the sign of Lyapunov exponents as (+, +, −, −). Such (+, +, −, −) sign of Lyapunov exponents is in contradiction with the well known (+, +, 0, −) sign of Lyapunov exponents for a 4-D hyperchaotic system. This paper thus discusses various issues related to Lyapunov exponents and proves that the reported sign of (+, +, −, −) Lyapunov exponents is actually (+, +, 0, −) or (+, 0, −, −). This clarification is very important and essential since Lyapunov exponents are the only quantitative measure for the existence of hyperchaos. Three different algorithms are used for calculating the Laypunov exponents to prove the actual sign of Lyapunov exponents for a hyperchaotic system.

Keywords: Lyapunov exponents; Nature of Lyapunov exponents; Measure of hyperchaos (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:92:y:2016:i:c:p:73-85

DOI: 10.1016/j.chaos.2016.09.010

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