Approximation for limit cycles and their isochrons.
Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).
Demongeot
Jacques
J
Laboratoire TIMC, UMR CNRS 5525, Faculté de Médecine, Université Joseph-Fourier de Grenoble, 38700 La Tronche, France.
Françoise
Jean-Pierre
JP
D006706:Homeostasis; D007700:Kinetics; D008954:Models, Biological; D008962:Models, Theoretical