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There exist extensive studies on periodic and random perturbations of variouscontinuous maps investigating their dynamics. This paper presents a randompiecewise smooth map derived from a simple inductor-less switching circuit. Thebifurcation parameter is bounded and randomly selected from a stationarydistribution. Due to the stochasticity inherent in either the parameter valuesor the state variable, the time evolution of the state variable cannot bepredicted at a specific time instant. We observe that the state variableexhibits completely ergodic behavior when the minimum value of the parameter is2.0. However, the ensemble average of the state variable converges to a fixedvalue. For parameter values ranging from 2.0 to 3.5, the system demonstratesnonchaotic behavior, and the absolute value of the Lyapunov exponent increasesmonotonically with the asymmetry (ap) of the distribution from which thebifurcation parameter values are sampled. We determine the probability densityfunction of the random map and verify its invariance under any initialcondition. The most noteworthy result is the disappearance of chaotic behaviorwhen the lower range of the distribution is varied while maintaining a fixedupper threshold for a particular distribution, even though the nonrandom mapexhibits an array of periodic and chaotic behaviors within that range.

Exploring Chaos and Ergodic behavior of an Inductorless Circuit driven by Stochastic Parameters