caa a22 4500 445361131 CHVBK 20180317142915.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s11071-010-9799-y doi (NATIONALLICENCE)springer-10.1007/s11071-010-9799-y Song Yongli Department of Mathematics, Tongji University, 200092, Shanghai, China aut Hopf bifurcation and spatio-temporal patterns indelay-coupled van der Pol oscillators [Elektronische Daten] [Yongli Song] In this paper, the dynamics of a pair of van der Pol oscillators with delayed velocity coupling is studied by taking the time delay as a bifurcation parameter. We first investigate the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay, and then study the direction and stability of the Hopf bifurcations. Then by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups, we investigate the spatio-temporal patterns of Hopf bifurcating periodic oscillations. We find that there are different in-phase and anti-phase patterns as the coupling time delay is increased. The analytical theory is supported by numerical simulations, which show good agreement with the theory. Springer Science+Business Media B.V., 2010 van der Pol oscillator nationallicence Delay nationallicence Stability switches nationallicence Hopf bifurcation nationallicence Spatio-temporal patterns nationallicence Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 223-237 0924-090X 63:1-2<223 2011 63 11071 https://doi.org/10.1007/s11071-010-9799-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9799-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Song Yongli Department of Mathematics, Tongji University, 200092, Shanghai, China aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/1-2(2011-01-01), 223-237 0924-090X 63:1-2<223 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer