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Articles, 4 records found
Articles 4 records found  
1.
On the "traveling pulses" of the limit of the FitzHugh-Nagumo equation when ɛ→0 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
A solution (u(s), v(s)) of the differential system u = v, v = −cv−u(u−a)(1−u) + w, w = −(ɛ/c)(u−γw) with a, c, ɛ ∈ R such that (u(s), v(s)) → (0,0) when s → ± ∞ is a traveling pulse of the FitzHugh-Nagumo equation. [...]
2023 - 10.1016/j.nonrwa.2023.103891
Nonlinear Analysis: Real World Applications, Vol. 73 (October 2023) , art. 103891  
Detailed record - Creative Commons
2.
16 p, 793.8 KB Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China))
In this paper, we study the dynamics of the FitzHugh-Nagumo system x˙=z,y˙=b(x-dy),z˙=x(x-1)(x-a)+y+cz having invariant algebraic surfaces. This system has four different types of invariant algebraic surfaces. [...]
2021 - 10.1007/s00033-020-01450-1
Zeitschrift fur Angewandte Mathematik und Physik, Vol. 72, Issue 1 (February 2021) , art. 15  
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3.
7 p, 614.8 KB Periodic solutions of a periodic FitzHugh-Nagumo differential system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bio Bio(Chile). Departamento de Matemática)
Recently some interest has appeared for the periodic FitzHugh-Nagumo differential systems. Here, we provide sufficient conditions for the existence of periodic solutions in such differential systems.
2015 - 10.1142/S0218127415501801
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25 Núm. 13 (2015) , p. 1550180 (6 pages)  
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4.
15 p, 712.5 KB Zero-Hopf bifurcation in the Fitzhugh-Nagumo system / D. Euzébio, Rodrigo (UNESP(Brazil). Departament de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bio Bio(Chile). Departamento de Matemática)
We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+ and P− in the FitzHugh-Nagumo system. Thus we find two 2-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. [...]
2014 - 10.1002/mma.3365
Mathematical methods in the applied sciences, 2014  
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