Convergence of Neural Networks with a Class of Real Memristors with Rectifying Characteristics

The paper considers a neural network with class of real extended memristors obtained via the parallel connection an ideal memristor and nonlinear resistor. resistor has same rectifying characteristic for current as that used in relevant models literature to account diode-like effects at interface between metal insulating material. proves some fundamental results on trajectory convergence this networks under assumption interconnection matrix satisfies symmetry conditions. First all, shows that, while case memristors, it is possible explicitly find functions state variables are invariants motions, can be Lyapunov decrease along trajectories characteristics. This property then study by means reduction-of-order technique combination approach. theoretical predictions verified numerical simulations, illustrated applications solution image processing tasks time.