Ezequiel del Rio's research

Some publications included in the ISI Journal Citation Reports: (if your institution has no electronic subscription to the links below, please contact me for reprints)

Index:

Papers on intermittency theory.
Papers on Strange, fractal and chaotic attractors.
Papers on Brownian ratchets and stochastic methods.

Experimental papers using electronic circuits:

Papers on Toda-solitons.

Papers on chaotic dynamics.

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Papers on intermittency theory:

The intermittency is a classical route to chaos, classified at the beginning in three types. To develop the main results on the intermittency systems' behaviour was assumed a constant value for a typical probability relative to the trajectories of this systems. We show that, in general, it is not true, hence we generalise the classical results about intermittencies of types I, II and III.

Ezequiel del Rio, Sergio Elaskar (2016),
"On the Theory of Intermittency in 1D Maps"
International Journal of Bifurcation and Chaos, 26, 1650228

DOI: 10.1142/S021812741650228X .

Abstract

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Recently, we reported how the reinjection probability density (RPD) can be generalized. Estimation of the universal RPD is based on ﬁtting a linear function to experimental or numerical data. Here we present an analytical approach to estimate the RPD. After this, we can get an analytic evaluation of the characteristic exponent traditionally used to characterize the intermittency type. The proposed theoretical method is general and very simple to use. It is compared with numerical computation, showing a good agreement between both. Our analytical results are compared with some celebrated classical numerical results on intermittency theory.

Sergio Elaskar,Ezequiel del Rio and Andrea Costa (2017),
"Reinjection Probability Density for Type-III Intermittency With Noise and Lower Boundary of Reinjection"
Journal of Computational and Nonlinear Dynamics 12, 031020

DOI: 10.1115/1.4034732 .

Abstract

In this paper, we extend a methodology developed recently to study type-III intermittency considering different values of the noise intensity and the lower boundary of reinjection (LBR). We obtain accurate analytic expressions for the reinjection probability density (RPD). The proposed RPD has a piecewise definition depending on the nonlinear behavior, the LBR value, and the noise intensity. The new RPD is a sum of exponential functions with exponent α + 2, where α is the exponent of the noiseless RPD. The theoretical results are verified with the numerical simulations.

Sergio Elaskar,Ezequiel del Rio and Eduardo Zapico (2016),
"Evaluation of the statistical properties for type-II intermittency using the Perron–Frobenius operator"
Nonlinear Dynamics 86, 1107

DOI: 10.1007/s11071-016-2951-6 .

Abstract

In this paper, we study type-II intermittency by means of the Perron–Frobenius operator. We calculate analytical expressions for the reinjection probability density (RPD) and the probability density of the laminar lengths (RPDLs) for several maps with type-II intermittency. The proposed theoretical RPDs and RPDLs are verified by numerical simulations. We carry out comparisons between the new RPD and RPDL functions with those obtained by a recent developed methodology which uses an auxiliary function (M(x) function methodology). Finally, we found the advantages and difficulties of both methodologies: Perron–Frobenius operator and M(x) function.

Sergio Elaskar,Ezequiel del Rio, Gustavo Krause and Andrea Costa (2015),
"Effect of the lower boundary of reinjection and noise in Type-II intermittency"
Nonlinear Dynamics 79, 1411–1424

DOI: 10.1007/s11071-014-1750-1 .

Abstract

We implement a recent methodology to study type-II intermittency considering different val- ues of the lower boundary of reinjection (LBR) and the noise intensity. With this approach, analytical expres- sions for the reinjection probability density (RPD) are accurately obtained. The proposed RPD has a piecewise deﬁnition addressing the different reinjec- tion mechanisms appearing in the system depending on the LBR value and the noise intensity. Also, the new probability density of the laminar lengths is calculated. When LBR = 0, the noisy probability density of the laminar lengths presents a cutoff, which disappears for noise strength different to zero. The theoretical results are veriﬁed with numerical simulations.

Ezequiel del Rio, Sergio Elaskar and Jose M. Donoso (2014),
"Laminar length and characteristic relation in Type-I intermittency"
Commun Nonlinear Sci Numer Simulat. 19, 967-976

DOI: 10.1016/j.cnsns.2013.08.012 .

Ezequiel del Rio, Sergio Elaskar and Valeri A. Makarov (2013),
"Theory of intermittency applied to classical pathological cases",
CHAOS. 23, 033112.

DOI: 10.1063/1.4813857.

Ezequiel del Rio, Miguel A.F. Sanjuán and Sergio Elaskar (2012),
"Effect of noise on the reinjection probability density in intermittency",
Commun Nonlinear Sci Numer Simulat. 17, 3587-3596.

DOI: 10.1016/j.cnsns.2012.01.020.

S. Elaskar, Ezequiel del Rio, and J. M. Donoso (2011),
"Reinjection Probability Density in Type-III Intermittency".
Physica A. 390, 2759-2768.

DOI: 10.1016/j.physa.2011.03.016.

Ezequiel del Rio and Sergio Elaskar (2010),
"New Characteristic Relations in Type-II Intermittency".
International Journal of Bifurcation and Chaos. 20, 1185-1191.
Sergio Elaskar and Ezequiel del Rio (2009),
"Reinjection probability function with lower bound of the reinjection for intermittency type III".
Mecánica Computacional. XXVIII, 1463-1475.

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Papers on Strange, fractal and chaotic attractors:

Ezequiel del Rio and J. M. Donoso (2008),
"Note on Strange Nonfractal Attractors"
International Journal of Bifurcation and Chaos. 18, 3657-3663.
( A fractal set is not piecewise differentiable. The contrary, that is "a not piecewise differentiable set is a fractal set" seems to be true. This is because the not piecewise differentiable set found at the beginning, think about Weierstrass and Kock set, until now, are fractal sets. However, in this publication we present a counterexample, that is "a not piecewise differentiable and nonfractal set". )

O. Lopez-Rebollal,J.R. Sanmartin and Ezequiel del Rio (1998),
"Sudden transition to chaos in plasma wave interactions."
Physics of plasmas. 15, 2861-2867.

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Papers on Brownian ratchets and stochastic methods:

Ezequiel del Rio , Manuel G. Velarde and Werner Ebeling, (2007).
"Dissipative solitons, wave asymmetry and dynamical ratchets"
Physica A. 337, 435- 447.

J . M. Donoso and Ezequiel del Rio (2007).
"Propagator solvers for Vlasov-Fokker-Planck equations"
Journal of Physics A. 40, 449-456.

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Experimental papers using electronic circuits:

Papers on Toda-solitons:

Ezequiel del Rio , V. A. Makarov, W. Ebeling and M. G. Velarde (2003).
"Mode transitions and wave propagation in a driven-dissipative Toda-Rayleigh ring."
Physical Review E. 67, 056208 1-9

V. A. Makarov, Ezequiel del Rio , W. Ebeling and M. G. Velarde (2001).
"Toda-Rayleigh lattice and its oscillatory modes."
Physical Review E. 64, 036601 1-12

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Papers on chaotic dynamics:

Ezequiel del Rio , J. R. Sanmartin and O. López-Rebollal. (1998).
"Experimental evidence of a hard transition to chaos"
International Journal of Bifurcation and Chaos. 18, 2225-2262.

Ezequiel del Rio , M.G. Velarde and A. Rodríguez-Lozano. (1994).
"Long Time Data Series and Difficulties with the Characterization of Chaotic Attractors: a Case with Intermitency III"
Chaos, Solitons & Fractals. 4, 2169-2179 .

Ezequiel del Rio , M.G. Velarde, A. Rodríguez-Lozano, N.F. Rul'kov, A.R. Volkovskii. (1994).
"Experimental Evidence for Synchronous Behavior of Chaotic Nonlinear Oscillator with Unidirectional or Mutual Driving"
International Journal of Bifurcations and Chaos. 4, 1003-1009.

Ezequiel del Rio , A. Rodríguez-Lozano and M.G. Velarde. (1994).
"Melnikov Criterion and its Experimental Test Using a Nonlinear Oscillator"
Chaos, Solitons & Fractals. 4, 255-262.

Ezequiel del Rio , A. Rodríguez-Lozano and M.G. Velarde. (1994).
"Note on the Stability of Limit Cycles of on Asymmetric (Helmholtz-Thompson) Nonlinear Oscillator"
Journal of Sound and Vibration. 4, 283-287.

N.F. Rul'kov, A.R. Volkovskii, A. Rodríguez-Lozano, Ezequiel del Rio and M.G. Velarde. (1994).
"Synchronous Chaotic Behavior of a Response Oscillator with a Chaotic Driving."
Chaos Solitons & Fractals. 4, 201-211.

Ezequiel del Rio , A. Rodríguez-Lozano and M.G. Velarde. (1992).
"A Prototype Helmholtz-Thompson Nonlinear Oscillator."
Review of Scientific Instruments. 63, 4208 -4212.

N.F. Rul'kov, A.R. Volkovskii, A. Rodríguez-Lozano, Ezequiel del Rio and M.G. Velarde. (1992).
"Mutual Synchronization of Chaotic Self-Oscillator with Dissipative Coupling."
International Journal of Bifurcations and Chaos. 2, 669-676.

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