Acta Universitaria

Number (NE-2), 2013

3-8
Local fractional variational iteration method for Fokker-Planck equation on a Cantor

Authors: Xiao Jun Yang, Dumitru Baleanu

Abstract

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Number of views: 411

Recently the local fractional operators have started to be considered a useful tool to deal with fractal functions defined on Cantor sets. In this paper, we consider the Fokker-Planck equation on a Cantor set derived from the fractional complex transform method. Additionally, the solution obtained is considered by using the local fractional variational iteration method.

9-11
Population dynamics with fractional equations (Predator-Prey)

Authors: Leticia Ramírez Hernández, Mayra Guadalupe García Reyna, Juan Martínez Ortiz

Abstract

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Number of views: 492

The main objective is to analyze the Predator-Prey model from the fractional calculus perspective. Fractional calculus is a tool for modeling phenomena associated with non-locality. The fractional model developed in Rivero, Trujillo, Vázquez & Velasco (2011), which considers abnormal situations in population growth, will be used.

12-15
Dynamics of the helmholtz oscillator with fractional order damping

Authors: Adolfo Ortiz, Jesús Seoane, J. Yang, Miguel Sanjuán

Abstract

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Number of views: 372

The dynamics of the nonlinear Helmholtz Oscillator with fractional order damping are studied in detail. The discretization of differential equations according to the Grünwald-Letnikov fractional derivative definition in order to get numerical simulations is reported. Comparison between solutions obtained through a fourth-order Runge-Kutta method and the fractional damping system are comparable when the fractional derivative of the damping term a is fixed at 1. That proves the good performance of the numerical scheme. The effect of taking the fractional derivative on the system dynamics is investigated using phase diagrams varying a from 0.5 to 1.75 with zero initial conditions. Periodic motions of the system are obtained at certain ranges of the damping term. On the other hand, escape of the trajectories from a potential well result at a certain critical value of the fractional derivative. The history of the displacement as a function of time is shown also for every a selected.

16-18
The theorem existence and uniqueness of the solution of a fractional differential equation

Authors: Juan Martínez Ortiz, Leticia Ramírez Hernández

Abstract

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Number of views: 413

This article aims to demonstrate, using the Picard-Banach theorem, the proof of the theorem-based existence and uniqueness of the solution of an fractional orden differential equation with a fractional Caputo-type derivative.

19-22
Modeling the tumor growth with the theory of discrete fractional calculus

Authors: Leticia Ramírez Hernández, Juan Martínez Ortiz

Abstract

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Number of views: 605

In this paper we describe the basics of modeling the growth of cancerous tumors, based on the formalism of the calculation of fractional order differences. Version is used in the Gompretz equation of differences, a simulation with arbitrary values of the growth rates of decline and the initial value.

23-26
Study of rogue wave by low-pass filtered noise in a multistable fiber laser

Authors: R. Sevilla Escoboza, G. Huerta Cuéllar, J. García López, D. López Mancilla, C. Castañeda Hernández, A. Pisarchik

Abstract

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Number of views: 401

Clear evidence of rogue waves in a multistable system is revealed with an erbium-doped fiber laser driven by harmonic pump modulation (Pisarchik, Jaimes-Reátegui, Sevilla-Escoboza, Huerta-Cuellar & Taki, 2011). We demonstrate numerically and experimentally that a low-pass noise filtering can control the probability for the appearance of a particular state. The results of numerical simulations with the use of a three-level laser model display good agreement with experimental results. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon.

27-31
Bifurcation in calculus of variations with constraints

Authors: Panayotis Vyridís

Abstract

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Number of views: 466

We describe a variational problem on a domain of a plane under a constraint of geometrical character. We provide sufficient and necessary conditions for the existence of bifurcation points. The problem in 2 coordinate form, corresponds to a quasilinear elliptic boundary value problem. The problem provides a physical model for several applications referring to continuum media and membranes.

32-35
Experimental noise-induced on-off intermittency in two bidirectionally-coupled diode lasers

Authors: Alfredo Campos Mejía, Alexander Pisarchik

Abstract

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Number of views: 401

Intermittent switches between chaotic and steady-state regimes are observed in experiments with two mutually-coupled diode lasers subject to common white gaussian noise. Both time series and power spectrum analyses yield typical scaling laws for on-off intermittency.

36-39
Amplitude variation in fractional multiple-interference on N-beams

Authors: E. Alvarado Méndez, M. Trejo Durán, J. M. Estudillo Ayala, R. Rojas Laguna

Abstract

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Number of views: 376

Multiple periodic patterns by light interference are a complicated problem from an experimental point of view. We report a theoretical model of the incidence of N beams of light at one point in space. Two components of the electric field are projected: azimuthal (angle formed with the projection of the vector in space on the x-y plane) and zenithal (angle of the incident vector with the z-axis). As a result, azimuthal intensity and zenithal intensity are found. The case of fractional amplitude or fractional number of beams is analyzed. When the phase is modified, the process allows us to visualize the change of geometry. Quasi-lineal patterns to maximum and minimum concentric circles are observed. Some applications of these patterns can be found in sensors and engraving in some lithography processes.

40-44
Numerical study of few-cycle pulses generation from supercontinuum in ANDi-PCF

Authors: O. Shulika, I. Sukhoivanov, S. Iakushev, I. Guryev, J. Andrade Lucio, O. Ibarra Manzano, A. Barrientos García, G. Ramos Ortiz

Abstract

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Number of views: 442

This paper presents the design of all-normal dispersion photonic-crystal fiber optimized for pulse-preserving supercontinuum generation near 800 nm. The supercontinuum generation is analyzed numerically addressing the role of pump pulse energy and the pump wavelength deviation from the zeroth point of third-order dispersion. We have also shown that supercontinuum generated in designed ANDi-PCF from a few nanojoule 100 fs pulses can be efficiently compressed down to a sub-10-fs pulse with a simple quadratic compressor.

45-47
Implementation of a dynamically flexible optoelectronics logic gate using a fiber laser, numerical study

Authors: S. Afanador Delgado, R. Jaimes Reátegui, R. Sevilla Escoboza, G. Huerta Cuéllar, J. García López, D. López Mancilla, L. Camacho Castillo, C. Castañeda Hernández

Abstract

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Number of views: 415

We implement an algorithm to reproduce the behavior of a dynamic logic gate which consists of three elements: a fiber laser in chaotic regime, a threshold controller and the output of the logic gate. The output signal of the fiber laser is sent to the logic gate input as to the threshold controller; threshold controller output signal is sent at the entrance of the logic gate and also fed back to the fiber laser which changes their dynamic behavior. The output of the logic gate consists of a difference amplifier; this compares the signals sent by the threshold controller and the fiber laser, resulting logic output that depend on an accessible parameter in threshold controller. We present the numerical results of the implementation of a dynamic logic gate using fiber laser, which demonstrates the ability to change the type of logic gate by modifying a parameter of threshold control.

48-50
Huber-Braun neuron dynamics

Authors: V. Vera-Ávila, R. Jaimes Reátegui, R. Sevilla Escoboza, G. Huerta-Cuéllar, J. García-López, D. López Mancilla, L. Camacho Castillo, C. Castañeda Hernández, A. Pisarchik

Abstract

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Number of views: 455

We study a physiologically realistic implementation of internal stochasticity in a four dimensional Hodgkin-Huxley (HH) type model of cold receptors. We show that in a deterministically tonic-firing regime, changing the parameters can drive the neuron into a state of complex bursting behavior. An explanation of the mechanism behind this effect is given in terms of a bifurcation diagram of inter-spike interval (ISI) as the temperature and external current are altered.