Generalized multistable structure via chaotic synchronization and preservation of scrolls

Jiménez-López, Eusebio; Salas, J. S. González; Ontañón-García, L. J.; Campos-Cantón, E.; Pisarchik, Alexander N.

doi:10.1016/j.jfranklin.2013.06.025

Cited by 16 publications

(10 citation statements)

References 26 publications

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“…As the authors in [23] mentioned, the above Definitions 2.1 and 2.2 imply that the UDS Type I is stable in one of its components but unstable in the other two, which are oscillatory. The converse is the UDS Type II, which are stable and oscillatory in two of its components but unstable in the other one.…”

Section: Hybrid Dynamical Systemmentioning

confidence: 98%

Electronic implementation of a dynamical network with nearly identical hybrid nodes via unstable dissipative systems

Anzo-Hernández

García-Martínez

Campos-Cantón

et al. 2019

Chaos, Solitons & Fractals

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A circuit architecture is proposed and implemented for a dynamical network composed of a type of hybrid chaotic oscillator based on Unstable Dissipative Systems (UDS). The circuit architecture allows selecting a network topology with its link attributes and to study, experimentally, the practical synchronous collective behavior phenomena. Additionally, based on the theory of dynamical networks, a mathematical model of the circuit was described, taking into account the natural tolerance of the electronic components. The network is analyzed both numerically and experimentally according to the parameters mismatch between nodes.

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Section: Hybrid Dynamical Systemmentioning

confidence: 98%

Electronic implementation of a dynamical network with nearly identical hybrid nodes via unstable dissipative systems

Anzo-Hernández

García-Martínez

Campos-Cantón

et al. 2019

Chaos, Solitons & Fractals

Self Cite

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“…number of scrolls along any of the axes if the above considerations are made when designing the system and locating equilibria along the axes in the following way [17,14]. First, start considering c 0 = 0 (in case that the first equilibrium point is located at the origin) and the value of c 1 = 0.…”

Section: Generation Of Scrolls Along Xmentioning

confidence: 99%

Multistability in Piecewise Linear Systems versus Eigenspectra Variation and Round Function

Gilardi-Velázquez

Ontañón-García

Hurtado-Rodriguez

et al. 2017

Int. J. Bifurcation Chaos

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A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to locate the corresponding equilibria among each of the commutation surfaces. These surfaces are generated by means of the switching function dividing the space in regions equally distributed along one axis. The trajectory of this type of system is governed by the eigenspectra of the coefficient matrix which can be adjusted by means of a bifurcation parameter. The behaviour of the system can change from multi-scroll attractors into a mono-stable state to the coexistence of several single-scroll attractors into a multi-stable state.Numerical results of the dynamics and bifurcation analyses of their parameters are displayed to depict the multi-stable states.

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“…In [29], it is shown that based on the number of linear pieces in the function ( ), the orbit of the system (14) and (15) could flow with the same number of scrolls. For the numerical integration made with multistable oscillator, the form (16) is applied and in most cases, the assigned values to the system (14) parameters are chosen to generate orbit solutions with shapes of three scroll oscillators.…”

Section: Multistable Systemmentioning

confidence: 99%

Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm

González-Salas

Shbat

Ordaz-Salazar

et al. 2016

Mathematical Problems in Engineering

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A numerical study that uses detrended fluctuation analysis (DFA) algorithm of time series obtained from linear and nonlinear dynamical systems is presented. The DFA algorithm behavior toward periodic and chaotic signals is investigated and the effect of the time scale under analysis is discussed. The displayed results prove that the DFA algorithm response is invariant (stable performance) to initial condition and chaotic system parameters. An initial idea of DFA algorithm implementation for fine spectrum sensing (SS) is proposed under two-stage spectrum sensor approach with test statistics based on the scaling exponent value. The outcomes demonstrate a promising new SS technique that can alleviate several imperfections such as noise power uncertainty and spatial correlation between the adjacent antenna array elements.

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Generalized multistable structure via chaotic synchronization and preservation of scrolls

Cited by 16 publications

References 26 publications

Electronic implementation of a dynamical network with nearly identical hybrid nodes via unstable dissipative systems

Electronic implementation of a dynamical network with nearly identical hybrid nodes via unstable dissipative systems

Multistability in Piecewise Linear Systems versus Eigenspectra Variation and Round Function

Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm

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