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第13行： − Ermentrout-Kopell规范模型被称为“θ模型”，是一个简单的神经元尖峰的一维模型。它与二次积分和放电神经元密切相关。模型的形式如下:图1:极限环上的鞍节点。模型的输入在哪里。变量在单位圆上，取值范围在0到神经元“刺突”即产生动作电位之间。 + 第216行：
第218行： − − − ==References== − − *W. Chester, The forced oscillations of a simple pendulum, J. Inst. Maths. Appl. '''15''' (1975) 298-306. − − *G.B. Ermentrout and N. Kopell, Parabolic bursting in an excitable system coupled with a slow oscillation, SIAM-J.-Appl.-Math, '''46''' (1986), 233-253. − − *B. Ermentrout, Type I membranes, phase resetting curves, and synchrony. Neural-Comput. '''8''', (1996) 979-1001 − − *F.C. Hoppensteadt, E.M. Izhikevich, Synchronization of MEMS resonators and mechanical neurocomputing, IEEE Trans. Circs. Systems, '''48''' (2001) 133-138. − − *F. C. Hoppendsteadt and E.M. Izhikevich (1997) Weakly Connected Neural Networks. Springer-Verlag, NY. − − *J. Stoker, Nonlinear Vibrations, Interscience, 1951. − − *F.M. Salam, J.E. Marsden, P.P. Varaiya, Arnold diffusion in the swing equations of a power system, IEEE Trans. Circuits and Systems, '''31''' (1984) 673-688. − − *A.J. Viterbi, Principles of Coherent Communication, McGraw-Hill, New York, 1966. − − *P. Horowitz, W. Hill, The Art of Electronics, Camb. U. Press, 1989. − − *R.P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, Addison-Wesley, Menlo Park, 1965. − − '''Internal references''' − − *Yuri A. Kuznetsov (2006) Andronov-Hopf bifurcation. Scholarpedia, 1(10):1858. − − *John Guckenheimer (2007) Bifurcation. Scholarpedia, 2(6):1517. − − *Valentino Braitenberg (2007) Brain. Scholarpedia, 2(11):2918. − − *James Meiss (2007) Dynamical systems. Scholarpedia, 2(2):1629. − − *Eugene M. Izhikevich (2007) Equilibrium. Scholarpedia, 2(10):2014. − − *Harold Lecar (2007) Morris-Lecar model. Scholarpedia, 2(10):1333. − − *James Murdock (2006) Normal forms. Scholarpedia, 1(10):1902. − − *Jeff Moehlis, Kresimir Josic, Eric T. Shea-Brown (2006) Periodic orbit. Scholarpedia, 1(7):1358. − − *Yuri A. Kuznetsov (2006) Saddle-node bifurcation. Scholarpedia, 1(10):1859. − − *Philip Holmes and Eric T. Shea-Brown (2006) Stability. Scholarpedia, 1(10):1838. − − *Frank Hoppensteadt (2006) Voltage-controlled oscillations in neurons. Scholarpedia, 1(11):1599. −
无编辑摘要
The '''Ermentrout-Kopell canonical model''' is better known as the "theta model" and is a simple one-dimensional model for the spiking of a [[neuron]]. It is closely related to the [[quadratic integrate and fire neuron]]. The model takes the following form:
The '''Ermentrout-Kopell canonical model''' is better known as the "theta model" and is a simple one-dimensional model for the spiking of a [[neuron]]. It is closely related to the [[quadratic integrate and fire neuron]]. The model takes the following form:
Ermentrout-Kopell规范模型被称为“θ模型”，是一个简单的'''神经元'''尖峰的一维模型。它与'''二次积分和放电神经元'''密切相关。模型的形式如下:
:<math>\label{theta}
:<math>\label{theta}
where <math> I(t) </math> are the inputs to the model. The variable <math> \theta </math> lies on the unit circle and ranges between 0 and <math>2\pi\ .</math> When <math> \theta=\pi </math> the neuron "spikes", that is, it produces an [[action potential]].
where <math> I(t) </math> are the inputs to the model. The variable <math> \theta </math> lies on the unit circle and ranges between 0 and <math>2\pi\ .</math> When <math> \theta=\pi </math> the neuron "spikes", that is, it produces an [[action potential]].
图1:极限环上的鞍节点。模型的输入在哪里。变量在单位圆上，取值范围在0到神经元“刺突”即产生'''动作电位'''之间。
==Derivation==
==Derivation==
[[Category:Models of Neurons]]
[[Category:Models of Neurons]]
[[Category:Eponymous]]
[[Category:Eponymous]]
==See Also==
==See Also==
Integrate-and-fire neuron, Neural excitability, Quadratic integrate-and-fire neuron, Saddle-node on invariant circle bifurcation, Voltage-controlled oscillations in neurons
Integrate-and-fire neuron, Neural excitability, Quadratic integrate-and-fire neuron, Saddle-node on invariant circle bifurcation, Voltage-controlled oscillations in neurons