Stability of differential equations associated with a class of one dimensional maps
M. C. Valsakumar, A. Rajan Nambiar, P. Rameshan
Abstract
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability. Generalization of the truncated models with N = 3 and 4 shows dynamical behaviour characteristic of systems with a riddled parameter space.
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