21 citations · 110 across the 20 of their papers we have counts for
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The One-dimensional Version of Peixoto's Structural Stability Theorem: A Calculus-based Proof
Aminur Rahman, Denis Blackmore
Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems,…
Stochastic discrete dynamical model for the hydrodynamic analog of a quantum mirage
Gonzalo Ferrandez Quinto, Aminur Rahman
Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statist…
Walking droplets as a damped-driven system
Aminur Rahman, J. Nathan Kutz
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, includi…
Generalized Attracting Horseshoe in the Rössler Attractor
Karthik Murthy, Parth Sojitra, Aminur Rahman +2
We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations - realizable by a rather simple electronic circuit - capable of producing a gen…
Exotic Bifurcations Inspired by Walking Droplet Dynamics
Aminur Rahman, Denis Blackmore
We identify two rather novel types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifold…
Peixoto's Structural Stability Theorem: The One-dimensional Version
Aminur Rahman
Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems,…
Discrete Dynamical Modeling and Analysis of the R-S Flip-Flop Circuit
Denis Blackmore, Aminur Rahman, Jigar Shah
A simple discrete planar dynamical model for the ideal (logical) R-S flip-flop circuit is developed with an eye toward mimicking the dynamical behavior observed for actual physical…