B K Roy, NIT Silchar, INDIA
The Lyapunov dimension is a well-defined quantitative measure using the Lyapunov exponents that may be used to classify nonlinear systems. For example, if the Lyapunov dimension of a system is equal to the number of states, then the system is said to be a conservative system; else, it will be a dissipative system. For nonlinear systems, (+, +, 0, -), (+, 0, -, -), (+, 0, -) and (0, -, -) natures of the Lyapunov exponents refer to a hyperchaotic system, a chaotic system, a chaotic system and a system with a limit cycle, respectively. The corresponding Lyapunov dimensions are 3+, 2+, 2+ and 1+. However, it has been observed in the literature that Lyapunov dimension 1+ is also called chaos. The presence of a positive Lyapunov exponent, like (+, -, -, -) or (+, -, -), is termed chaos without the due importance to the Lyapunov dimensions.
This presentation will first highlight a review of the nature of Lyapunov exponents and their inconsistent interpretations. A solution to such inconsistency will be attempted then. Finally, the classification of nonlinear systems using the Lyapunov dimension will be discussed.