scholarly journals Existence of a $T$-Periodic Solution for the Monodomain Model Corresponding to an Isolated Ventricle Due to Ionic-Diffusive Relations

2022 ◽  
Vol 177 (1) ◽  
Author(s):  
Andrés Fraguela ◽  
Raúl Felipe-Sosa ◽  
Jacques Henry ◽  
Manlio F. Márquez
Keyword(s):  
Periodic Solution ◽  
Monodomain Model ◽  
Isolated Ventricle

scholarly journals Existence of global solutions in a model of electrical activity of the monodomain type for a ventricle

Nova Scientia ◽  
2018 ◽  
Vol 10 (21) ◽  
pp. 17-44
Author(s):  
Ozkar Hernández Montero ◽  
Andrés Fraguela Collar ◽  
Raúl Felipe Sosa
Keyword(s):  
Weak Solution ◽  
Electrical Activity ◽  
Strong Solution ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Membrane Method ◽  
Monodomain Model ◽  
Isolated Ventricle ◽  
Definition Of

Introduction: A monodomain model of electrical activity for an isolated ventricle is formulated. This model is written as a reaction diffusion PDE coupled to an ODE, The Rogers-Mculloch model is used to represent the electrical activity through the cell membrane.                      Method: We give a definition of weak and strong solution of the variational Cauchy problem associated to the monodomain model. A sequence of approximate solutions of Faedo-Galerkin type is proposed.Results: It is shown that the sequence of approximate solutions converge to a weak solution according to the proposed definition. Finally, we have that this weak solution is also a strong solution.                        Conclusion: The monodomain model of electrical activity in an isolated ventricle that is proposed has a weak solution in an appropriate sense. In addition, this weak solution is also a strong solution. 

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

The Existence and Stability Analysis of Periodic Solution of Izhikevich Model

2020 ◽  
Vol 18 (5) ◽  
pp. 1161-1176
Author(s):  
Yi Li ◽  
Chuandong Li ◽  
Zhilong He ◽  
Zixiang Shen
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Existence And Stability ◽  
Izhikevich Model
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