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arXiv · 2304.08208

Fractional Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems

Sachin Bhalekar·Prashant M. Gade
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Abstract

We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on product $ab$. The conditions are much complex for fractional maps and depend on $ab$ as well as $a+b$. There are no superstable period-2 orbits. These conditions are useful in obtaining stability conditions of asymptotically periodic orbits with period-$2$ in the nonlinear case. The stability conditions are demonstrated numerically. The formalism can be generalized to higher periods.

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Sachin Bhalekar, Prashant M. Gade. 2023-04-17. Fractional Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems. https://arxiv.org/abs/2304.08208

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