Eur. Phys. J. Special Topics 228, 1943-1950 (2019)
https://doi.org/10.1140/epjst/e2019-800205-3

Regular Article

Detecting bifurcation points in a memristive neuron model

¹ Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi 537000, P.R. China
² Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
³ Ministry of Higher Education and Scientific Research, Baghdad, Iraq
⁴ NAAM Research Group, King Abdulaziz, University of Jeddah, Jeddah, Saudi Arabia
⁵ Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

^a e-mail: fahimenazarimehr@yahoo.com

Received: 20 November 2018
Received in final form: 5 February 2019
Published online: 14 October 2019

Abstract

In this paper, bifurcations of a memristive neuron model are analyzed. The system shows different limit cycles and chaotic attractors by varying external current. The focus of this paper is finding bifurcation points of the system and predicting them using critical slowing down indicators. The system has different tipping points such as transition from a period-2 limit cycle to period-3 limit cycle, period-3 limit cycle to period-6 limit cycle and limit cycle to chaos. Two critical slowing down indicators have been used to predict tipping points of the system. The first critical slowing down indicator is autocorrelation at lag-1 which cannot indicate bifurcation points of the system. The second one is Lyapunov exponent which shows acceptable results in prediction of bifurcation points of the memristive neuron model.