Bifurcation and recurrent analysis of memristive circuits

Bifurcation analysis is a powerful tool for studying nonlinear problems. However, its superiorities may short when considering acquired data sets instead of controllable chaos generator signals. In this case recurrent and statistical analysis may help to investigate the system. In this paper we compare several methods for estimation of number of scrolls in a memristive circuit model with the multi-scroll chaotic attractor. The techniques of histograms, kernel density estimation, moving average and recurrent analysis are considered. Two high-resolution dynamical maps are presented for the investigated circuit. The moving average method was found to be the most reliable and accurate method for constructing dynamical maps. The results of the work can be used for hidden attractor detection, multiwing systems research and studying other aspects of nonlinear dynamical systems.

[1]  Leon O. Chua,et al.  Simplest Chaotic Circuit , 2010, Int. J. Bifurc. Chaos.

[2]  Nikolay V. Kuznetsov,et al.  Hidden attractors in Dynamical Systems. From Hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits , 2013, Int. J. Bifurc. Chaos.

[3]  Baker Mohammad,et al.  Memristors for digital, memory and neuromorphic circuits , 2013, 2013 25th International Conference on Microelectronics (ICM).

[4]  Guangyi Wang,et al.  A Chaotic Oscillator Based on HP Memristor Model , 2015 .

[5]  A. I. Karimov,et al.  Computer simulation of chaotic systems with symmetric extrapolation methods , 2015, 2015 XVIII International Conference on Soft Computing and Measurements (SCM).

[6]  Denis N. Butusov,et al.  Study of two-memristor circuit model with explicit composition method , 2017, 2017 24th IEEE International Conference on Electronics, Circuits and Systems (ICECS).

[7]  Denis N. Butusov,et al.  Comparing the algorithms of multiparametric bifurcation analysis , 2017, 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM).

[8]  Chongxin Liu,et al.  Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system* , 2017 .

[9]  Denis N. Butusov,et al.  Numerical analysis of memristor-based circuits with semi-implicit methods , 2017, 2017 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus).

[10]  Dmitriy A. Belkin,et al.  Study of two-memcapacitor circuit model with semi-explicit ODE solver , 2017, 2017 21st Conference of Open Innovations Association (FRUCT).