An adaptive energy regulation in a memristive map linearized from a circuit with two memristive channels

Nonlinear circuits can show multistability when a magnetic flux-dependent memristor(MFDM) or a charge-sensitive memristor(CSM) is incorporated into a one branch circuit,which helps estimate magnetic or electric field effects.In this paper,two different kinds of memristors are incorporated into two branch circuits composed of a capacitor and a nonlinear resistor,thus a memristive circuit with double memristive channels is designed.The circuit equations are presented,and the dynamics in this oscillator with two memristive terms are discussed.Then,the memristive oscillator is converted into a memristive map by applying linear transformation on the sampled time series for the memristive oscillator.The Hamilton energy function for the memristive oscillator is obtained by using the Helmholtz theorem,and it can be mapped from the field energy of the memristive circuit.An energy function for the dual memristive map is suggested by imposing suitable weights on the discrete energy function.The dynamical behaviors of the new memristive map are investigated,and an adaptive law is proposed to regulate the firing mode in the memristive map.This work will provide a theoretical basis and experimental guidance for oscillator-to-map transformation and discrete map energy calculation.

A Control Problem for Nonstationary Population Systems

In this paper,we study the nonstationary population control systems:We regard the female-sum fertility rate β(t) as control auction ac judge its optimality by"norm minimum",and discuss the minimum norm control problems for the above population control systems.Utilizing space L2(0,T)’s reflexivity,smoothness and strict convexity,we prove the existence,the uniqueness and the approximation property of the minimum norm control for the nonstationary population control systems and give the corresponding optimality conditions by means of the methods of the dial mapping of Banach space.