Controlling Chaos

The objective of this presentation is to showcase the possibility of controlling a chaotic system. We will start by demonstrating a particular control mechanism that can stabilize the chaotic dynamics and show results from two systems (the double scroll oscillator and the Hindmarsh-Rose neural system) in a chaotic parameter regime. The outcome of this control is the emergence of periodic orbits called cupolets (chaotic unstable periodic orbit-lets), which will persist as long as the control mechanism is applied. We will expand on this research to examine the behavior of multiple interconnected HR neurons communicating via the control scheme. Our results indicate that pairs and even networks of HR neurons can be stabilized by controlling a single target neuron.