ROUTES TO CHAOS IN A MODEL OF A BURSTING NEURON

被引:72
作者
CANAVIER, CC [1 ]
CLARK, JW [1 ]
BYRNE, JH [1 ]
机构
[1] UNIV TEXAS,SCH MED,DEPT NEUROBIOL & ANAT,HOUSTON,TX 77225
关键词
D O I
10.1016/S0006-3495(90)82643-6
中图分类号
Q6 [生物物理学];
学科分类号
071011 ;
摘要
Chaotic regimens have been observed experimentally in neurons as well as in deterministic neuronal models. The R15 bursting cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. Previously, the model of Plant and Kim has been shown to exhibit both bursting and beating modes of electrical activity. In this report, we demonstrate (a) that a chaotic regime exists between the bursting and beating modes of the model, and (b) that the model approaches chaos from both modes by a period doubling cascade. The bifurcation parameter employed is the external stimulus current. In addition to the period doubling observed in the model-generated trajectories, a period three "window" was observed, power spectra that demonstrate the approaches to chaos were generated, and the Lyaponov exponents and the fractal dimension of the chaotic attractors were calculated. Chaotic regimes have been observed in several similar models, which suggests that they are a general characteristic of cells that exhibit both bursting and beating modes. © 1990, The Biophysical Society. All rights reserved.
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收藏
页码:1245 / 1251
页数:7
相关论文
共 41 条
[1]   VOLTAGE AND ION DEPENDENCES OF THE SLOW CURRENTS WHICH MEDIATE BURSTING IN APLYSIA NEURON R15 [J].
ADAMS, WB ;
LEVITAN, IB .
JOURNAL OF PHYSIOLOGY-LONDON, 1985, 360 (MAR) :69-93
[2]   SPONTANEOUS ACTIVITY IN ISOLATED SOMATA OF APLYSIA PACEMAKER NEURONS [J].
ALVING, BO .
JOURNAL OF GENERAL PHYSIOLOGY, 1968, 51 (01) :29-+
[3]   BURSTING PHENOMENA IN EXCITABLE MEMBRANES [J].
CARPENTER, GA .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1979, 36 (02) :334-372
[4]   ABNORMAL DISCHARGES AND CHAOS IN A NEURONAL MODEL SYSTEM [J].
CHAY, TR .
BIOLOGICAL CYBERNETICS, 1984, 50 (04) :301-311
[6]   CHAOS IN A 3-VARIABLE MODEL OF AN EXCITABLE CELL [J].
CHAY, TR .
PHYSICA D, 1985, 16 (02) :233-242
[7]   BURSTING, BEATING, AND CHAOS IN AN EXCITABLE MEMBRANE MODEL [J].
CHAY, TR ;
RINZEL, J .
BIOPHYSICAL JOURNAL, 1985, 47 (03) :357-366
[8]  
Conrad M, 1986, CHAOS, P3
[9]  
CVITANOVIC P, 1984, UNIVERSALITY CHAOS, P3
[10]   QUANTITATIVE UNIVERSALITY FOR A CLASS OF NON-LINEAR TRANSFORMATIONS [J].
FEIGENBAUM, MJ .
JOURNAL OF STATISTICAL PHYSICS, 1978, 19 (01) :25-52