Bifurcation analysis of a Morris–Lecar neuron model

• Published in: Biological cybernetics Vol. 108; no. 1; pp. 75 - 84
• Main Authors: Liu, Congmin, Liu, Xuanliang, Liu, Shenquan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2014; Springer; Springer Nature B.V
• Subjects: Action Potentials - physiology; Algorithms; Alterations; Animals; Applied sciences; Artificial intelligence; Bifurcations; Bioinformatics; Biological and medical sciences; Biomedical and Life Sciences; Biomedicine; Bistability; Central nervous system; Central neurotransmission. Neuromudulation. Pathways and receptors; Complex Systems; Computer Appl. in Life Sciences; Computer science; control theory; systems; Computer simulation; Connectionism. Neural networks; Cybernetics; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; Humans; Mathematical models; Membranes; Models, Neurological; Neural networks; Neurobiology; Neurons; Neurons - physiology; Neurosciences; Numerical analysis; Original Paper; Vertebrates: nervous system and sense organs; Bifurcation; Morris–Lecar model; Limit cycle; Bistability; Alteration; Excitability; Neural network; Periodic solution; Modeling; Morris-Lecar model
• ISSN: 0340-1200; 1432-0770
• DOI: 10.1007/s00422-013-0580-4

In this paper, we investigate the dynamical behaviors of a Morris–Lecar neuron model. By using bifurcation methods and numerical simulations, we examine the global structure of bifurcations of the model. Results are summarized in various two-parameter bifurcation diagrams with the stimulating current as the abscissa and the other parameter as the ordinate. We also give the one-parameter bifurcation diagrams and pay much attention to the emergence of periodic solutions and bistability. Different membrane excitability is obtained by bifurcation analysis and frequency-current curves. The alteration of the membrane properties of the Morris–Lecar neurons is discussed.