F Ur Mathematik in Den Naturwissenschaften Leipzig Attractor Switching by Neural Control of Chaotic Neurodynamics Attractor Switching by Neural Control of Chaotic Neurodynamics

Chaotic attractors of discrete-time neural networks include innnitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between diierent stabilized periodic orbits. For chaotic modules with noise random switching between diierent periodic orbits is observed.