Interpreting initial offset boosting via reconstitution in integral domain

Abstract Initial offset boosting behaviors with homogenous, heterogeneous or extreme multistability have been reported in several nonlinear systems, but the forming mechanisms were rarely discussed. To figure out this problem, a four-dimensional (4-D) memristive system with cosine memductance is presented, which can exhibit initial offset boosting related to extreme multistability. Taking this 4-D memristive system as paradigm, a three-dimensional (3-D) system with standalone initials-related parameters is reconstructed in an integral domain. Thus, the original line equilibrium set is mapped as some periodically varied equilibrium points, which allows that the initial offset boosting is modeled as variable offset boosting with infinite topologically different attractors. Besides, the reconstituted 3-D model exhibits bi-stability or quadri-stability for fixed parameters, but it maintains the dynamics of the 4-D 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 reconstituted variable offset boosting behaviors.