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Volumn 2, Issue 1, 2008, Pages 24-32

Modelling excitable cells using cycle-linear hybrid automata

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; MATHEMATICAL MODELS; MORPHOLOGY; PIECEWISE LINEAR TECHNIQUES;

EID: 38949203802     PISSN: 17518849     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-syb:20070001     Document Type: Article
Times cited : (36)

References (34)
  • 2
    • 0027544543 scopus 로고
    • 'Smart cars on smart roads: Problems of control'
    • 0018-9286
    • Varaiya, P.: 'Smart caPs on smart roads: problems of control', IEEE Trans. Autom. Control, 1993, 38, (2), p. 195-270 0018-9286
    • (1993) IEEE Trans. Autom. Control , vol.38 , Issue.2 , pp. 195-270
    • Varaiya, P.1
  • 3
    • 38649093751 scopus 로고    scopus 로고
    • 'Design and evaluation of tools for automated highway systems'
    • LNCS 1066 (Springer-Verlag)
    • Deshpande, A., Godbole, D., Göllü, A., and Varaiya, P.: 'Design and evaluation of tools for automated highway systems', Hybrid systems III', LNCS 1066 (Springer-Verlag 1996), p. 138-148
    • (1996) Hybrid Systems III' , pp. 138-148
    • Deshpande, A.1    Godbole, D.2    Göllü, A.3    Varaiya, P.4
  • 5
    • 84957869487 scopus 로고    scopus 로고
    • 'An approach to the verification of the center-tracon automation system'
    • Springer-Verlag, London, UK
    • Lygeros, J., Pappas, G.J., and Sastry, S.: 'An approach to the verification of the center-tracon automation system', HSCC'98 Proc. First Int. Workshop on Hybrid Systems, 1998, Springer-Verlag, London, UK p. 289-304
    • (1998) HSCC'98 Proc. First Int. Workshop on Hybrid Systems , pp. 289-304
    • Lygeros, J.1    Pappas, G.J.2    Sastry, S.3
  • 9
    • 84944196766 scopus 로고    scopus 로고
    • 'Lateral inhibition through delta-notch signaling: A piecewise affine hybrid model'
    • Springer-Verlag, Rome, Italy 2034, Lecture Notes in Computer Science
    • Ghosh, R., and Tomlin, C.J.: 'Lateral inhibition through delta-notch signaling: A piecewise affine hybrid model', Hybrid Systems: Computation and Control: 4th Int. Workshop, 2001, Springer-Verlag, Rome, Italy 2034, Lecture Notes in Computer Science
    • (2001) Hybrid Systems: Computation and Control: 4th Int. Workshop
    • Ghosh, R.1    Tomlin, C.J.2
  • 11
    • 1642348388 scopus 로고    scopus 로고
    • 'A simplified model of propagation and dissipation of excitation fronts'
    • Biktashev, V.N.: 'A simplified model of propagation and dissipation of excitation fronts', Int. J. Bifurcation Chaos, 2003, 13, p. 3605-3619
    • (2003) Int. J. Bifurcation Chaos , vol.13 , pp. 3605-3619
    • Biktashev, V.N.1
  • 12
    • 0001976781 scopus 로고    scopus 로고
    • 'Vortex dynamics in 3d continous myocardium with fiber rotation: Filament instability and fibrillation'
    • 1054-1500
    • Fenton, F., and Karma, A.: 'Vortex dynamics in 3d continous myocardium with fiber rotation: Filament instability and fibrillation', CHAOS, 1998, 8, p. 20-47 1054-1500
    • (1998) CHAOS , vol.8 , pp. 20-47
    • Fenton, F.1    Karma, A.2
  • 13
    • 35649001607 scopus 로고
    • 'A quantitative description of membrane currents and its application to conduction and excitation in nerve'
    • Hodgkin, A.L., and Huxley, A.F.: 'A quantitative description of membrane currents and its application to conduction and excitation in nerve', J. Physiol, 1952, 117, p. 500-544
    • (1952) J. Physiol , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 14
    • 0028233422 scopus 로고
    • 'A dymanic model of the cardiac ventricular action potential: I. simulations of ionic currents and concentration changes'
    • Luo, C.H., and Rudy, Y.: 'A dymanic model of the cardiac ventricular action potential: I. simulations of ionic currents and concentration changes', Circuits. Res., 1994, 74, p. 1071-1096
    • (1994) Circuits. Res. , vol.74 , pp. 1071-1096
    • Luo, C.H.1    Rudy, Y.2
  • 16
    • 38949091597 scopus 로고    scopus 로고
    • 'Hybrid automata as a unifying framework for modeling cardiac cells'
    • Ye, P., Entcheva, E., Smolka, S.A., True, M., and Grosu, R.: 'Hybrid automata as a unifying framework for modeling cardiac cells', Proc. EMBC, 2006
    • (2006) Proc. EMBC
    • Ye, P.1    Entcheva, E.2    Smolka, S.A.3    True, M.4    Grosu, R.5
  • 18
    • 4444326589 scopus 로고    scopus 로고
    • 'Taming the complexity of biochemical models through bisimulation and collapsing: Theory and practice'
    • Antoniotti, M., Piazza, C., Policriti, A., Simeoni, M., and Mishra, B.: 'Taming the complexity of biochemical models through bisimulation and collapsing: Theory and practice', Theory. Comput. Sci., 2004, 325, (1), p. 45-67
    • (2004) Theory. Comput. Sci. , vol.325 , Issue.1 , pp. 45-67
    • Antoniotti, M.1    Piazza, C.2    Policriti, A.3    Simeoni, M.4    Mishra, B.5
  • 19
    • 84958171885 scopus 로고    scopus 로고
    • 'Reachability analysis of hybrid systems via predicate abstraction'
    • Alur, R., Dang, T., and Ivancic, F.: 'Reachability analysis of hybrid systems via predicate abstraction', HSCC, 2002, p. 35-48
    • (2002) HSCC , pp. 35-48
    • Alur, R.1    Dang, T.2    Ivancic, F.3
  • 20
    • 14344265954 scopus 로고    scopus 로고
    • 'Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling: Delta-notch protein signaling'
    • Ghosh, R., and Tomlin, C.J.: 'Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling: Delta-notch protein signaling', IEE Trans. Syst. Biol., 2004, 1, (1), p. 170-183
    • (2004) IEE Trans. Syst. Biol. , vol.1 , Issue.1 , pp. 170-183
    • Ghosh, R.1    Tomlin, C.J.2
  • 21
    • 34047104160 scopus 로고    scopus 로고
    • 'Modeling the electrical activity of a neuron by a continuous and piecewise affine hybrid system'
    • Dumas, J.G., and Rondepierre, A.: 'Modeling the electrical activity of a neuron by a continuous and piecewise affine hybrid system', Hybrid Systems: Computation and Control, 2003, p. 156-171
    • (2003) Hybrid Systems: Computation and Control , pp. 156-171
    • Dumas, J.G.1    Rondepierre, A.2
  • 22
    • 0035711016 scopus 로고    scopus 로고
    • 'Stability and reachability analysis of a hybrid model of luminescence in the marine bacterium vibrio fischeri'
    • Belta, C., Schug, J., and Dang, T.: 'Stability and reachability analysis of a hybrid model of luminescence in the marine bacterium vibrio fischeri', 40th IEEE Conf. Decision and Control, 2001, 1, p. 869-874
    • (2001) 40th IEEE Conf. Decision and Control , vol.1 , pp. 869-874
    • Belta, C.1    Schug, J.2    Dang, T.3
  • 23
    • 53349102813 scopus 로고
    • 'Impulses and physiological states in theoretical models of nerve membrane'
    • 0006-3495
    • FitzHugh, R.: 'Impulses and physiological states in theoretical models of nerve membrane', Biophys. J., 1961, 1, p. 445-467 0006-3495
    • (1961) Biophys. J. , vol.1 , pp. 445-467
    • FitzHugh, R.1
  • 24
    • 6344238035 scopus 로고
    • 'An active pulse transmission line simulating nerve axon'
    • Nagumo, J., Arimoto, S., and Yoshizawa, S.: 'An active pulse transmission line simulating nerve axon', Proc of the IRE, 1962, 50, (10), p. 2061-2070
    • (1962) Proc of the IRE , vol.50 , Issue.10 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 25
    • 0000688571 scopus 로고
    • 'Nagumo's equation'
    • Mckean, H.P.: 'Nagumo's equation', Adv. Math., 1970, 4, p. 209-223
    • (1970) Adv. Math. , vol.4 , pp. 209-223
    • Mckean, H.P.1
  • 26
    • 0000559545 scopus 로고
    • 'Systems of differential equations, containing small parameters at the derivatives'
    • Tikhonov, A.N.: 'Systems of differential equations, containing small parameters at the derivatives', Mat. Sbornik, 1952, 31, (3), p. 575-586
    • (1952) Mat. Sbornik , vol.31 , Issue.3 , pp. 575-586
    • Tikhonov, A.N.1
  • 27
    • 0000898198 scopus 로고
    • 'The asymptotic behaviour of systems of differential equations with a small parameter multiplying the highest derivatives'
    • Pontryagin, L.S.: 'The asymptotic behaviour of systems of differential equations with a small parameter multiplying the highest derivatives', Izv. Akad. Nauk SSSR, Ser. Mat., 1957, 21, (5), p. 107-155
    • (1957) Izv. Akad. Nauk SSSR, Ser. Mat. , vol.21 , Issue.5 , pp. 107-155
    • Pontryagin, L.S.1
  • 28
    • 84891949264 scopus 로고    scopus 로고
    • 'Comparison of asymptotics of heart and nerve excitability'
    • Article no. 011902
    • Suckley, R., and Biktashev, V.N.: 'Comparison of asymptotics of heart and nerve excitability', Phys. Rev. E, 2003, 68, (011902), p. 1-15
    • (2003) Phys. Rev. E , vol.68 , pp. 1-15
    • Suckley, R.1    Biktashev, V.N.2
  • 30
    • 33750856807 scopus 로고    scopus 로고
    • 'Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model'
    • Courtemanche, M., Ramirez, R.J., and Nattel, S.: 'Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model', Am. J. Physiol., 1998, 275, p. 301-321
    • (1998) Am. J. Physiol. , vol.275 , pp. 301-321
    • Courtemanche, M.1    Ramirez, R.J.2    Nattel, S.3
  • 31
    • 33646203778 scopus 로고    scopus 로고
    • 'Conditions for propagation and block of excitation in an asymptotic model of atrial tissue'
    • 0006-3495
    • Simitev, R.D., and Biktashev, V.N.: 'Conditions for propagation and block of excitation in an asymptotic model of atrial tissue', Biophys. J., 2006, 90, p. 2258-2269 0006-3495
    • (2006) Biophys. J. , vol.90 , pp. 2258-2269
    • Simitev, R.D.1    Biktashev, V.N.2
  • 32
    • 38949092744 scopus 로고    scopus 로고
    • 'Efficient event-driven simulation of excitable hybrid automata'
    • True, M., Entcheva, E., Smolka, S.A., Ye, P., and Grosu, R.: 'Efficient event-driven simulation of excitable hybrid automata', Proc. EMBC, 2006
    • (2006) Proc. EMBC
    • True, M.1    Entcheva, E.2    Smolka, S.A.3    Ye, P.4    Grosu, R.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.