INTRODUCTION In 1992 i was inspirated,reading the text ofBalth Van Der Polabout relaxation oscillation.Balth Van Der Pol is first to propose a cardiac simulator with electronic tubes at year 1928.The 24 may 1928,Balth Van Der Pol gives a conference at paris,invited be the biologycal society and the electrical society of France.The integral text of the con& ference is published at journal Onde Electrique,and,intituled,the heart can be considered like a relaxation oscillation and an electrical model of the heart.At this time of 1992,my min dis kept on by the diable of heart and relaxation oscillation.So i have on mind to discover acardiac simulator,like Balth Van Der Pol,and i will call it,cardiorythmor.My dream is realized in 2005 when i publish in France 2 patents on an elec& tronic and machanic cardiac simulator.(seewww.inpi.fr,www.espacenet. com).I begin to study the cardiac cells electrophysiology,so i find for the first time tje names of,A.L.Hodgkin and A.F.Huxley.Hodgkin and Huxley was first to propose a mathamatical model ,and an electrical model for the cardiac cells in 1952.Latter in 1962 they receive the nobel price for his work.For learning cardiac electrophysiology i request to be integrated in clinical cardiology of Dantec hospital in dakar senegal. Si i would like to express my great thanks to DR Semou diouf,Moustapha sarr,Bara Ibrahima diop,Fallou cisse,Gora seck,and Ba. A)in the volume 1 i present the theoritical basic foundation of what would be the cardiac science theory,when we apply the results of dynamic system, stability,existence of periodic solution,existence of hysterisis cycle,existen& ce of chaos,and to verify with my models all the properties of the heart,and to observe in simulations all the knowed phenomenon of the heart and the unknowed.I propose a parametrized mathematical model and an associated electrical circuit,called themodel pacemaker VI1,in non linear ODE equations, dV/dt=P(V,I1,K) dI1/dt=Q(V,I1,K) Where V is the potential of the membrane cells,I1 is an excitable variable and K is the set of 8 cardiac parameters.I proove the existence of stable periodic solution,the existence of chao and bifurcation,and observe in simulations all the properties of the heart like,electrical stimulation,and blocks.The model is integrated with runge kutta 4 and matlab software R2007a.
To take in consideration the existence of basic ion currents,Na forso+ dium,and ,K for potassium,I propose themodel pacemaker VINAIK. B)in the volume 2 i investigate chao in phase plan ofHenri Poincare, and propose a parametrized mathematical model and electrical model of the heart calledheart VI1. C)in the volume 3 i modelize the propagation of cardiac excitation with PDE,partial differential equations and propose methods to construct periodical solution and non periodical solutions. I dedicace my work to my professors at lyon 1 and university paris orsay, Mr Andre Blanc Lapierre,Mr Bernard Picinbono,Mr Debraine INSTN Saclay,Mr Gabet and Mr Bonnemay. ‘’In my life i had to have one question i really love ‘’ Bob Marley ‘’One day,he sings at london,the next day to paris,the day after at belgium,and the next day to spanish,working for the next day’’. D.P.L.NDao