A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators

Van der Pol, 1928, The heartbeat considered as a relaxation-oscillation and an electrical model of the heart, Phil. Mag., 6, 763, 10.1080/14786441108564652 Van der Pol, 1929, The heartbeat considered as a relaxation-oscillation and an electrical model of the heart, Arch. Neerl. Physiol., 14, 418 Van der Pol, 1940, Biological rhythms considered as relaxation oscillations, Acta Med. Scand. Suppl., 108, 76 Winfree, 1967, Biological rhythms and the behavior of populations of coupled oscillators, J. Theor. Biol., 16, 15, 10.1016/0022-5193(67)90051-3 Roberge, 1971, A cardiac pacemaker model, Med. Biol. Eng., 9, 3, 10.1007/BF02474399 Rosenberg, 1970, Nonlinear models for normal and abnormal heart rhythms. Developments in mechanics, Vol. 6, 91 Grant, 1956, The mechanism of A-V arrhythmias with an electronic analogue of the human A-V node, Amer. J. Med., 20, 334, 10.1016/0002-9343(56)90118-8 Bhereur, 1971, A simulation unit for cardiac arrhythmias, Med. Biol. Eng., 9, 13, 10.1007/BF02474400 Urthaler, 1973, Mathematical relationship between automaticity of the sinus node and the AV junction, Amer. Heart J., 86, 189, 10.1016/0002-8703(73)90243-3 Urthaler, 1974, Electrophysiological and mathematical characteristics of the escape rhythm during complete AV block, Cardiovasc. Res., 8, 173, 10.1093/cvr/8.2.173 James, 1963, The connecting pathways between the sinus node and A-V node and between the right and left atrium in the human heart, Amer. Heart J., 66, 498, 10.1016/0002-8703(63)90382-X Liénard, 1928, Etudes des oscillations entretenues, Rev. Gén. Elec., 109 Levinson, 1943, On a non-linear differential equation of the second order, J. Math. Phys., 22, 41, 10.1002/sapm194322141 Dorodnicyn, 1947, Asymptotic solution of Van der Pol's equation, Prikl. Mat. Mekh., 11, 313 Urabe, 1960, Periodic solutions of Van der Pol's equation with dampling coefficient λ = 0 ∼ 10, IRE Trans. Circuit Theory, CT-7, 382, 10.1109/TCT.1960.1086718 Urabe, 1960, Remarks on periodic solutions of Van der Pol's equation, J. Sci. Hiroshima Univ., 24, 197, 10.32917/hmj/1555639762 Krogdahl, 1960, Numerical solution of the Van der Pol equation, Z. Angew. Math. Phys., 11, 59, 10.1007/BF01591803 Gear, 1971, DIFSUB for solution of ordinary differential equations, Comm. ACM, 14, 185, 10.1145/362566.362573 Shampine, 1972, Some numerical experiments with DIFSUB, ACM Signum Newsletter, 7, 24, 10.1145/1052668.1052674 Shampine, 1973, Local extrapolation in the solution of ordinary differential equations, Math. Comp., 27, 91, 10.1090/S0025-5718-1973-0331803-1 Shampine, 1974, Limiting precision in differential equation solvers, Math. Comp., 28, 141, 10.1090/S0025-5718-1974-0329308-8 James, 1973, The sinus node as a servomechanism, Circ. Res., 32, 307, 10.1161/01.RES.32.3.307 Urthaler, 1973, Comparative dependence on adrenergic neural tone by automaticity in the sinus node and in the atrioventricular junction, J. Pharmacol. Exp. Ther., 187, 269 Roberge, 1969, The nature of Wenckebach cycles, Canad. J. Physiol. Pharmacol., 47, 695, 10.1139/y69-119