Dynamical systems (DS) is a mathematical formalization of the general scientific concept of a deterministics process. DS includes a set of its possible states and a law of the evolution of the state in time (Kuznetsov, 1998).

Publications:

• Carrillo, H., & Hoppensteadt, F. (2010). Unfolding an electronic integrate-and- fire circuit . Biological cybernetics, 102(1), 1-8.
• Carrillo Calvet, Humberto, Mendoza Reyes, Miguel Angel & Ongay Larios, Fernando. (2004). Integrate-and-Fire Neurons and Circle Maps . WSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE, 1(2), 287-293.
• Carrillo Calvet, Humberto, & Ongay Larios, Fernando.(2001). On the firing maps of a general class of forced integrate and fire neurons . Mathematical Biosciences, 172, 33-53.
• Barriga Montoya, Carolina, Carrillo Calvet, Humberto, & Ongay Larios, Fernando. (2003). El Modelo de FitzHugh-Nagumo para el Potencial Eléctrico de una Neurona. . Aportaciones Matemáticas, Serie de Comunicaciones, 32, 31-49.
• Carrillo Calvet, Humberto, & Ongay Larios, Fernando. (2001). On the firing maps of a general class of forced integrate and fire neurons. . Mathematical Biosciences, 172, 33-53
• Agüero, M. , Frias, G. & Ongay Larios, Fernando. (2000). Generalized Coherent States and Nonlinear Dynamics of a Lattice Quasispin Model . Chaos Solitons & Fractals, 11, 2203-2213.
• Carrillo Calvet, Humberto, & Guzmán, José Ramón. (1999). A Dynamical Systems Proof of Euler's Generalization of the Little Fermat's Theorem . Aportaciones Matemáticas, Serie Comunicaciones, 25, 199-202.
• Carrillo Calvet, Humberto, & Guzmán, José Ramón. (1998). A Dynamical Systems Proof of the Little Theorem of Fermat . Aportaciones Matemáticas, Serie Comunicaciones, 22, 63-65.
• Baer, Steven M., Rinzel, John & Carrillo Calvet, Humberto. (1996) A Three Variable Autonomous Phase Model For Neuronal Parabolic Bursting . In Differential Equations With Aplications to Biology and Industry. World Scientific, Singapore, 1-11.
• Carrillo Calvet, Humberto, Rinzel, John & Baer, S. M. (1996). Nonlinear Oscillations in Neurons Models . EUROMECH -2nd European Nonlinear Oscillation Conference, Prague, Septiembre 9-13, 1996.
• Sienra Loera, Guillermo. (1996). On the dynamics of the one parameter functions Fa(z)=z*z+2az . Bol. Soc. Mat. Mexicana, 2(3).
• Baer, Steven M., Rinzel, John & Carrillo Calvet, Humberto. (1995). Analysis of an Autonomous Phase Model for Neuronal Parabolic Bursting . Journal of Mathematical Biology, 33, 309-333.
• Guzmán,José R., Carrillo Calvet, Humberto, & Ongay Larios, Fernando. (1994). Dinámica de las Iteraciones de la Función de Arnold . Aportaciones Matemáticas serie Comunicaciones, 14, 405-414.
• Carrillo Calvet, Humberto. (1988). The Averaging Method and the Persistence of Attractors . Applicable Analysis, 29, 191-208
• Carrillo Calvet, H.(1987). Perturbation Results on the Long Run Behavior of Nonlinear Dynamical Systems . Contemporary Mathematics, 58 (Part III), 1-9.
• Salinas Fernández, Emilio & Carrillo Calvet, Humberto. Modelos de la Actividad Neuroeléctrica . Memorias del II Ciclo de Conferencias sobre Neurocomputación Centro Nacional de Cálculo, Instituto Politécnico Nacional, México.
• Carrillo Calvet, Humberto. Averaging and Synchronization of Weakly Coupled System . Lecture Notes in Biomathematics, 66, 244-251.Carrillo Calvet, Humberto. Averaging and Synchronization of Weakly Coupled System. Lecture Notes in Biomathematics, 66, 244-251.