Aperiodic stochastic resonance in a hysteretic population of cardiac neurons

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 1816-1824

  Kember, G C ^a   Fenton, G A ^a   Collier, K ^a   Armour, J A ^a  

^a DALHOUSIE UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL MODEL; CYTOLOGY; HEART; HEART MUSCLE; HEART VENTRICLE PRESSURE; INNERVATION; MONTE CARLO METHOD; NERVE CELL; PHYSIOLOGY; STATISTICS; TIME;

HEART; MODELS, NEUROLOGICAL; MONTE CARLO METHOD; MYOCARDIUM; NEURONS; STOCHASTIC PROCESSES; TIME FACTORS; VENTRICULAR PRESSURE;

CIRCUIT RESONANCE; HYSTERESIS; MAGNETIC RESONANCE; STOCHASTIC SYSTEMS;

CAUSE AND EFFECTS; CONTROL PERFORMANCE; EXTERNAL FORCING; HIGHER NOISE LEVELS; HYSTERETIC SYSTEMS; INHIBITORY NEURONS; SEMI-ANALYTICAL MODEL; STOCHASTIC RESONANCES;

NEURONS;

EID: 0034137481     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.1816     Document Type: Article

References (25)

1. J.J. Collins, C.C. Chow, and T.T. Imhoff, Nature (London) 376, 236 (1995).
2. F. Moss, D. Pierson, and D. O’Gorman, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 1383 (1994).
3. J.J. Collins, C.C. Chow, and T.T. Imhoff, Phys. Rev. E 52, 3321 (1995).
4. M.T. Mahato and S.R. Shenoy, Phys. Rev. E 50, 2503 (1994).
5. A. Longtin, J. Stat. Phys. 70, 309 (1993).
6. C. Heneghan, C.C. Chow, J.J. Collins, T.T. Imhoff, S.B. Lowen, and M.C. Teich, Phys. Rev. E 54, 2228 (1996).
7. A.R. Bulsara and A. Zador, Phys. Rev. E 54, 2185 (1996).
8. J.E. Levin and J.P. Miller, Nature (London) 380, 165 (1996).
9. P.C. Gailey, A. Neiman, J.J. Collins, and F. Moss, Phys. Rev. Lett. 79, 4701 (1997).
10. H.A. Kramers, Physica (Amsterdam) 7, 284 (1940).
11. C.C. Chow, T.T. Imhoff, and J.J. Collins, Chaos 8, 616 (1998).
12. J.J. Collins, T.T. Imhoff, and P. Grigg, J. Neurophysiol. 76, 642 (1996).
13. A. Krawiecki and A. Sukiennicki, Chaos 8, 768 (1998).
14. J.J. Collins, C.C. Chow, A.C. Capela, and T.T. Imhoff, Phys. Rev. E 54, 5575 (1996).
15. H.R. Wilson and J.D. Cowan, Biophys. J. 12, 1 (1972).
16. J.A. Armour, in Reflex Control of the Circulation, edited by I.H. Zucker and J.P. Gilmore (CRC Press, Boca Raton, FL, 1991).
17. J.L. Ardell, C.K. Butler, F.A. Smith, D.A. Hopkins, and J.A. Armour, Am. J. Physiol. 260, 713 (1991).
18. M. Horackova and J.A. Armour, Cardiovasc. Res. 30, 326 (1995).
19. W.C. Randall, R.D. Wurster, D.C. Randall, and S.X. Xi-Moy, in Nervous Control of the Heart, edited by J.T. Shepherd and S.F. Vatner (Harwood Academic Publishers, Amsterdam, 1996).
20. J.A. Armour, K. Collier, G. Kember, and J.L. Ardell, Am. J. Physiol. 274, 939 (1998).
21. A.Y.K. Wong and J.A. Armour, Neural Networks 5, 35 (1992).
22. Depending on the parameters and the nature of the sigmoidal response functions (Formula presented) and (Formula presented) Eq. (1) can have hysteresis curves with more than two approximately constant steady “States” 15 (the capital S implies an approximately constant level is a State output analogous to State 1 or State 2 detailed in Fig. 22). The general description of a State requires only the time (Formula presented) to switch into that State from any State below (of smaller steady value) or above (of greater steady value).
23. The time (Formula presented) to switch states is also dependent to the order of the neuronal time constants on the initial conditions and details for when the solution of Eq. (1) is deemed to have switched states. Hence, (Formula presented) is resolved to the order of the neuronal time constants.
24. E. Vanmarcke, Random Fields (MIT Press, Cambridge, MA, 1984).
25. J.A. Armour, Cardiovasc. Res. 41, 41 (1999).