21 citations · 135 across the 22 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,…
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…
Generalized Attracting Horseshoes and Chaotic Strange Attractors
Yogesh Joshi, Denis Blackmore, Aminur Rahman
A generalized attracting horseshoe is introduced as a new paradigm for describing chaotic strange attractors (of arbitrary finite rank) for smooth and piecewise smooth maps f from…
Strange Attractors for Asymptotically Zero Maps
Yogesh Joshi, Denis Blackmore
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact…
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…