Hopf-bifurcation-delay-induced bursting patterns in a modified circuit system

[1]  Qinsheng Bi,et al.  Study of mixed-mode oscillations in a parametrically excited van der Pol system , 2014 .

[2]  Zhengdi Zhang,et al.  Routes to bursting in a periodically driven oscillator , 2013 .

[3]  Peter J. Menck,et al.  How basin stability complements the linear-stability paradigm , 2013, Nature Physics.

[4]  Qinsheng Bi,et al.  Generation of hysteresis cycles with two and four jumps in a shape memory oscillator , 2013 .

[5]  Kuniyasu Shimizu,et al.  Complex mixed-mode oscillations in a Bonhoeffer–van der Pol oscillator under weak periodic perturbation , 2012 .

[6]  Paul Woafo,et al.  Bursting oscillations in electromechanical systems , 2011 .

[7]  Qinsheng Bi,et al.  Bursting oscillations in Duffing’s equation with slowly changing external forcing , 2011 .

[8]  Denis de Carvalho Braga,et al.  Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor , 2009 .

[9]  Qing-ju Fan,et al.  Horseshoe in a modified Van der Pol-Duffing circuit , 2009, Appl. Math. Comput..

[10]  Zhuoqin Yang,et al.  Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis , 2008 .

[11]  Steven M Baer,et al.  Slow acceleration and deacceleration through a Hopf bifurcation: power ramps, target nucleation, and elliptic bursting. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  H. Agiza,et al.  Bifurcations, chaos and synchronization in ADVP circuit with parallel resistor , 2008 .

[13]  Andrey Shilnikov,et al.  Origin of bursting through homoclinic spike adding in a neuron model. , 2007, Physical review letters.

[14]  Huw G. Davies,et al.  A period–doubling bifurcation with slow parametric variation and additive noise , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  Martin Golubitsky,et al.  An unfolding theory approach to bursting in fast–slow systems , 2001 .

[16]  Eugene M. Izhikevich,et al.  Neural excitability, Spiking and bursting , 2000, Int. J. Bifurc. Chaos.

[17]  Richard Haberman,et al.  Slow Passage through a Saddle-Center Bifurcation , 2000, J. Nonlinear Sci..

[18]  G. J. M. Marée,et al.  Slow Passage Through a Pitchfork Bifurcation , 1996, SIAM J. Appl. Math..

[19]  Thomas Erneux,et al.  Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions , 1993, SIAM J. Appl. Math..

[20]  M. Georgiou.  Slow Passage Through Bifurcation and Limit Points. Asymptotic Theory and Applications in the Areas of Chemical and Laser Instabilities. , 1991 .

[21]  J. Rinzel,et al.  The slow passage through a Hopf bifurcation: delay, memory effects, and resonance , 1989 .

[22]  Thomas Erneux,et al.  The slow passage through a steady bifurcation: Delay and memory effects , 1987 .