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A smooth dynamical system that counts in binary

Mark R. Greenstreet, Xuemei Huang

Open publisher page 5 citations

Abstract

This paper presents a smooth dynamical system that implements a toggle flip-flop. The flip-flop is described as a system of smooth, non-linear ODEs. We identify a period-2, invariant set of this system, and show that this corresponds to the discrete state transitions of a discrete model. We show that this behaviour is robust for a large class of inputs and that these toggle elements can be composed to implement a binary counter of any number of bits.

About this research paper

What this paper is about

This paper presents a smooth dynamical system that implements a toggle flip-flop. The flip-flop is described as a system of smooth, non-linear ODEs. We identify a period-2, invariant set of this system, and show that this corresponds to the discrete state transitions of a discrete model. We show that this behaviour is robust for a large class of inputs and that these toggle elements can be composed to implement a binary counter of any number of bits.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

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Method / approach

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Available abstract

This paper presents a smooth dynamical system that implements a toggle flip-flop. The flip-flop is described as a system of smooth, non-linear ODEs. We identify a period-2, invariant set of this system, and show that this corresponds to the discrete state transitions of a discrete model. We show that this behaviour is robust for a large class of inputs and that these toggle elements can be composed to implement a binary counter of any number of bits.

Key concepts: Binary number, Invariant (physics), Computer science, Set (abstract data type), Class (philosophy), Dynamical systems theory, Algorithm, State (computer science)

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