caa a22 4500 445294841 CHVBK 20180317142538.0 cr unu---uuuuu 170323e20100901xx s 000 0 eng 10.1007/s11571-010-9116-y doi (NATIONALLICENCE)springer-10.1007/s11571-010-9116-y Approximate expressions of the bifurcating periodic solutions in a neuron model with delay-dependent parameters by perturbation approach [Elektronische Daten] [Min Xiao, Jinde Cao] This paper is interested in gaining insights of approximate expressions of the bifurcating periodic solutions in a neuron model. This model shares the property of involving delay-dependent parameters. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work so harder. Most existing methods for studying the nonlinear dynamics fail when applied to such a class of delay models. Although Xu etal. (Phys Lett A 354:126-136, 2006) studied stability switches, Hopf bifurcation and chaos of the neuron model with delay-dependent parameters, the dynamics of this model are still largely undetermined. In this paper, a detailed analysis on approximation to the bifurcating periodic solutions is given by means of the perturbation approach. Moreover, some examples are provided for comparing approximations with numerical solutions of the bifurcating periodic solutions. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only. Springer Science+Business Media B.V., 2010 Neuron model nationallicence Delay-dependent parameters nationallicence Approximation nationallicence Periodic solution nationallicence Perturbation approach nationallicence Xiao Min Department of Mathematics, Southeast University, 210096, Nanjing, People's Republic of China aut Cao Jinde Department of Mathematics, Southeast University, 210096, Nanjing, People's Republic of China aut Cognitive Neurodynamics Springer Netherlands 4/3(2010-09-01), 241-250 1871-4080 4:3<241 2010 4 11571 https://doi.org/10.1007/s11571-010-9116-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11571-010-9116-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Xiao Min Department of Mathematics, Southeast University, 210096, Nanjing, People's Republic of China aut NATIONALLICENCE 700 1- Cao Jinde Department of Mathematics, Southeast University, 210096, Nanjing, People's Republic of China aut NATIONALLICENCE 773 0- Cognitive Neurodynamics Springer Netherlands 4/3(2010-09-01), 241-250 1871-4080 4:3<241 2010 4 11571 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer