Abstract
Memristive oscillator systems are common models for many problems in physics, engineering, and systems biology. This paper presents a convergence analysis of two types of algorithms for solving a fourth-order memristive oscillator system. For the first algorithm, a parallel algorithm, a limiting state of the iterate sequence generated by a Jacobi iterative scheme and the Euler polygonal method, is a solution of the system under some weaker conditions. With the second algorithm, a partial difference method, which is based on the partial difference concept and exponential convergence, is also presented. The proposed algorithms in this paper can be applied to general nonlinear hybrid systems.
Highlights
A large number of applications for memristive oscillator systems have been reported, including nonvolatile memristor memories, digital and analog circuits; see [ – ].The models of memristive oscillator systems suggest possible responses of simple intelligences in biomimetics as well as new approaches for bio-inspired reconfigurable circuits.Considerable attention has been devoted to the theoretical properties of memristive oscillator systems, and their relationship to memristor dynamics
Deep studies of the memristive system are important in various applications due to the important guiding role in memristor-based physical commercially available devices
3 Partial difference method we present a constructive proof to illustrate the partial difference method and the related convergence analysis for system ( )
Summary
A large number of applications for memristive oscillator systems have been reported, including nonvolatile memristor memories, digital and analog circuits; see [ – ]. Considerable attention has been devoted to the theoretical properties of memristive oscillator systems, and their relationship to memristor dynamics (see [ – , , , ] and references therein). The memristive system is a complicated system that has strongly nonlinear behavior, as it includes the switched network cluster and shows a high uncertainty [ ]. Deep studies of the memristive system are important in various applications due to the important guiding role in memristor-based physical commercially available devices. Nonlinear dynamics has been shown to play an important role in the understanding of a wide spectrum of memristor-based technological and biological systems [ – , , – ]
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