Excitable systems with internal and coupling delays

Two delayed coupled excitable systems with internal delays are studied. For different parametric values each of the isolated units displays excitable, bi-stable or oscillatory dynamics. Bifurcational relations among coupling time-lag and coupling constant for different values of the internal time-lags are obtained. Possible types of synchronization between the units in typical dynamical regimes are studied.

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

[2]  Sue Ann Campbell,et al.  Stability and Bifurcation in the Harmonic Oscillator with Multiple, Delayed Feedback Loops , 1999 .

[3]  Nebojša Vasović,et al.  Type I vs. type II excitable systems with delayed coupling , 2005 .

[4]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[5]  N. Buric,et al.  Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Nikola Buric,et al.  Bifurcations due to Small Time-Lag in Coupled Excitable Systems , 2005, Int. J. Bifurc. Chaos.

[7]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[9]  Sen,et al.  Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators , 1998, Physical review letters.

[10]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[11]  K. Ikeda,et al.  High-dimensional chaotic behavior in systems with time-delayed feedback , 1987 .

[12]  Nebojsa Vasovic,et al.  Oscillations in an Excitable System with Time-Delays , 2003, Int. J. Bifurc. Chaos.

[13]  K. Gopalsamy,et al.  Delay induced periodicity in a neural netlet of excitation and inhibition , 1996 .

[14]  Sue Ann Campbell,et al.  Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation , 1994, SIAM J. Appl. Math..

[15]  I. Rogachevskii,et al.  Threshold, excitability and isochrones in the Bonhoeffer-van der Pol system. , 1999, Chaos.

[16]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[17]  Yurong Liu,et al.  Global asymptotic stability of generalized bi-directional associative memory networks with discrete and distributed delays , 2006 .

[18]  D. V. Reddy,et al.  Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators , 2000 .

[19]  Nikola Burić,et al.  Dynamics of delay-differential equations modelling immunology of tumor growth , 2002 .