A family of hyperchaotic multi-scroll attractors in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si25.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="bold">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>

Ontañón-García, L. J.; Jiménez-López, Eusebio; Campos-Cantón, E.

doi:10.1016/j.amc.2014.01.134

Cited by 33 publications

(20 citation statements)

References 35 publications

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“…In particular, we assume that the dimension n = 3 and that the eigenspectra of linear operators A τ ∈ R 3×3 have the following features: a) at least one eigenvalue is a real number; and 2) at least two eigenvalues are complex numbers. There is an approach to generate dynamical systems based on these linear dissipative systems (sometimes called an unstable dissipative system (UDS) [15]). In this paper we use a particular type of UDS called Type I : Definition 2.5.…”

Section: Piecewise Linear Dynamical Systemsmentioning

confidence: 99%

Itinerary synchronization between PWL systems coupled with unidirectional links

Anzo-Hernández

Campos-Cantón

Nicol

2019

Communications in Nonlinear Science and Numerical Simulation

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In this paper the collective dynamics of N -coupled piecewise linear (PWL) systems with different number of scrolls and coupled in a masterslave sequence configuration is studied, i.e. a ring connection with unidirectional links. Itinerary synchronization is proposed to detect synchrony behavior with systems that can present generalized multistability. Itinerary synchronization consists in analyzing the symbolic dynamics of the systems by assigning different numbers to the regions where the scrolls are generated. It is shown that in certain parameter regimes if the inner connection between nodes is given by means of considering all the state variables of the system, then itinerary synchronization occurs and the coordinate motion is determined by the node with the smallest number of scrolls. Thus the collective behavior in all the nodes of the network is determined by the node with least scrolls in its attractor leading to generalized multistability phenomena which can be detected via itinerary synchronization. Results about attacks to the network are also presented, for example, when the PWL system is attacked by removing a given link to produce an open ring configuration. Depending on the inner connection properties, the nodes present multistability or preservation in the number of scrolls of the attractors.

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Section: Piecewise Linear Dynamical Systemsmentioning

confidence: 99%

Itinerary synchronization between PWL systems coupled with unidirectional links

Anzo-Hernández

Campos-Cantón

Nicol

2019

Communications in Nonlinear Science and Numerical Simulation

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“…These manifolds are defined in a way that ϑ = (ϑ 1,2,3 ) is a set of column eigenvectors such that Aϑ i = λ i ϑ i with i = 1, 2, 3; E s = Span{ϑ 1 } and E u = Span{ϑ 2,3 }. In order to present such oscillations and following a similar mechanisms as in [6,16,7], two types of dissipative systems with unstable dynamics have been studied which will be called unstable dissipative systems (UDS), however only one type of both will be considered here. This type is defined in the following way:…”

Section: Uds Theorymentioning

confidence: 99%

“…(2) induces in the phase space R n the flow (φ t ) t∈R . Thus, each initial condition X 0 ∈ B generates a trajectory given by φ t (X 0 ) : t ≥ 0 which is trapped in an attractor A after defining at least two vectors B 1 and B 2 , as it is described in [16].…”

Section: Uds Theorymentioning

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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“…En general la histéresis se puede presentar o aplicar en sistemas de R n generando enroscados que pueden ser periódicos o hipercaóticos, lo cuales se originan por la conmutación de sistemas lineales [10], [11]. Sin embargo, en este trabajo se propone y se estudia un sistema lineal en dos variables (R 2 ) que conmuta dentro de una banda de histéresis para encontrar las configuraciones tanto de parámetros como de condiciones iniciales que permitan que el flujo del sistema genere una solución periódica dentro la banda histéresis.…”

Section: Figura 2: Control De Temperatura Por Ciclos De Histéresisunclassified

Dinámica de un sistema lineal en R2 conmutado por histéresis

2017

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ResumenEn este artículo se analiza el comportamiento local y global de un sistema dinámico suave a trozos en dos variables, estudiando el flujo de dos sistemas dinámicos lineales no homogéneos que conmutan con las fronteras de una banda de histéresis. Analíticamente se determinan las soluciones de equilibrio y los dominios paramétricos que garantizan la existencia de órbitas periódicas entre la banda. Se realizan simulaciones numéricas para obtener los retratos de fases y los dominios de atracción con diferentes valores de los parámetros. Los resultados muestran la coexistencia de múltiples estados estacionarios de diferente tipo para determinados valores de los parámetros.Palabras clave: Histéresis; órbita periódica; sistemas dinámicos suaves a trozos; dominios de atracción.

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A family of hyperchaotic multi-scroll attractors in Rn

Cited by 33 publications

References 35 publications

Itinerary synchronization between PWL systems coupled with unidirectional links

Itinerary synchronization between PWL systems coupled with unidirectional links

Multistability in Piecewise Linear Systems versus Eigenspectra Variation and Round Function

Dinámica de un sistema lineal en R2 conmutado por histéresis

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