| When the cosine memductance is introduced into nonlinear systems,oscillating circuits or neural morphological networks,it can induce periodically changed initial offset boosting behaviros,i.e.a special multistability phenomenon.This special initial-condition-denpendent dynamic property can provide more freedom for engineering applications of memristor systems,but its dynamic characteristics and formation mechanisms still need to be further analyzed and studied.In this paper,a novel class of memristor systems with cosine memductance is proposed,and the incremental integral transformation of state variables is used to reconstitute these systems.The periodically varied initial offset boosting behaviors and its formation mechanisms are analyzed in the original state variable domain and integral variable domain.Firstly,a four-dimensional one-memristor-based system is constructed based on memristor with cosine memductance.This system has a line equilibrium set,whose stability is periodically varied with the change of memristor-initial.The simulation results show that the memristor initial and other initial conditions can trigger nonlinear and one-dimensional initial offset boosting behaviors.In particular,along the boosting route,the system dispalys infinitely many coexisting attractors with different positions and topologies,resulting in the generation of extreme multistability.Furthermore,dimensional reduction modeling of the original four-dimensional memristive system is carried out using the incremental integral transformation method,and a three-dimensional reconstitution system is obtained,which expresses the initials condiitons of the original system as standalone system parameters.On this basis,the initial offset boosting behaviors with extreme multistability is reconstituted and analyzed.With fixed parameters,the reconstituted three-dimensional system exhibits bi-stability or quadri-stability,but it maintains the dynamics of the original four-dimensional memristive system when initiated from the neighborhood of the origin point.Finally,circuit synthesis,PSIM simulations,and experimental measurements are carried out to validate the offset boosting behaviors of the original and reconstituted systems.Secondly,a five-dimensional two-memristor-based Colpitts system is constructed by introducing two memristors with cosine memductance into the classical three-dimensional Colpitts oscillator model.The proposed memristive Colpitts system possesses a plane equilibrium set and their stabilities are periodically varied on the memristor initial plane.Moreover,the stability distribution patterns are evolved with the change of system control parameters.The numerically simulated results indicate that the system trajectories are confined by several unstable stability regions around the initiating point,leading to the generation of parameter and initial offset boosting dynamics.On this basis,a dimensionality reduction model with determined equilibrium is formulated through integral transformation of state variables.The parameter and initial offset boosting dynamics is reconstituted theoretically and expounded numerically in integral variable domain.Finally,an equivalent realization circuit is designed,and the above dynamical behaviors are verified by PSIM circuit simulations. |
