Abstract
A new fractal technique is used to investigate the onset of chaos in nonlinear dynamical systems. A comparison is made between this fractal technique and the commonly used Lyapunov exponent method. Agreement between the results obtained by both methods indicates that this technique may be used in a manner analogous to the Lyapunov exponents to predict onset of chaos. It is found that the fractal technique is much easier to implement than the Lyapunov method and it requires much less computational time. This fractal technique can easily be adopted to investigate the onset of chaos in many nonlinear dynamical systems and can be used to analyze theoretical and experimental time series.
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