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math.DS2026
Pantograph Difference Equations: Stability, Multistability, and Chaos
Prashant M. Gade, Sachin Bhalekar
Pantograph equations are functional differential equations with proportional delay, typically involving terms of the form , where . These equations have been studied…
math.DS2026
Maps of q-deformed fractional order: From circle to cardioid via crescent
Sachin Bhalekar, Prashant M. Gade
We introduce a class of \(q\)-deformed fractional order maps by replacing the classical binomial memory kernel in discrete fractional dynamics with Gaussian (\(q\)-) binomial coeff…