An overview of our prototype chaotic circuit and nonlinear control system is shown in Fig. 1. The chaotic circuit (known as the “plant” in the control literature) consists of passive components including diodes, capacitors, resistors, and inductors, and an active negative resistor realized with an operational amplifier that can source and sink power to the rest …
Classical reservoir computing We start with a nonlinear dynamical network of N variables of the following general form, $$\dot{{{{{{{{\bf{x}}}}}}}}}(t)={{{{{{{\boldsymbol{f}}}}}}}}[{{{{{{{\bf{x}}}}}}}}(t)],$$ (1) where \({{{{{{{\bf{x}}}}}}}}(t)={[{x}_{1}(t),\ldots,{x}_{N}(t)]}^{\top }\) denotes the N-dimensional (N-D) state of the system at time t, and \({{{{{{{\boldsymbol{f}}}}}}}}[{{{{{{{\bf{x}}}}}}}}(t)]={\left({f}_{1}[{{{{{{{\bf{x}}}}}}}}(t)],{f}_{2}[{{{{{{{\bf{x}}}}}}}}(t)],\ldots,{f}_{N}[{{{{{{{\bf{x}}}}}}}}(t)]\right)}^{\top }\) is the N-D nonlinear vector field. In this article, we assume that neither the vector field f (equivalently, …
Physical system of a magnetic device We consider a magnetic device of a thin rectangular system with cylindrical injectors (see Fig. 1c). The size of the device is L × L × D. Under the uniform external magnetic field, the magnetization is along the z direction. Electric current translated from time series data is injected at the Np injectors …