Chaos–hyperchaos transition in a class of models governed by Sommerfeld effect

Munteanu, Ligia; Brişan, Cornel; Chiroiu, Veturia; Dumitriu, Dan; Ioan, Rodica

doi:10.1007/s11071-014-1575-y

Cited by 17 publications

(5 citation statements)

References 35 publications

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“…This means that the motion is characterized by two attractors and at least one of which has a tendency towards chaos. This behavior is described in [23,24] for a class of models governed by the Sommerfeld effect and [25] for a Rössler chemical reaction system. The study of behavior of the structure under seismic loads is strongly related to active and passive control techniques.…”

Section: Analysis and Resultsmentioning

confidence: 99%

Sliding Mode Control and Geometrization Conjecture in Seismic Response

et al. 2021

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The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

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Section: Analysis and Resultsmentioning

confidence: 99%

Sliding Mode Control and Geometrization Conjecture in Seismic Response

et al. 2021

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“…These are the Milnor attractors [5], which are typically chaotic, possess locally unstable directions, and have strength zero [6]. One class of Milnor attractors are those with a riddled basin [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Specifically, for such an attractor, there exists a set of measure-zero points on it with trans-versely unstable dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, for any initial condition attracted to the Milnor attractor, there are initial conditions arbitrarily nearby that generate trajectories towards another attractor. The basin of the Milnor attractor is thus riddled with "holes" that belong to the basin of the other attractor, hence the term riddled basins [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Partially unstable attractors in networks of forced integrate-and-fire oscillators

Zou

Deng

et al. 2017

Nonlinear Dyn

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The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in nonlinear dynamics. In smooth dynamical systems, an attractor is often enclosed completely in its basin of attraction with a finite distance from the basin boundary. Recent works have uncovered that, in neuronal networks, unstable attractors with a remote basin can arise, where almost every point on the attractor is locally transversely repelling. Herewith we report our discovery of a class of attractors: partially unstable attractors, in pulsecoupled integrate-and-fire networks subject to a periodic forcing. The defining feature of such an attractor is that it can simultaneously possess locally stable and unstable sets, both of positive measure. Exploiting the structure of the key dynamical events in the network, we develop a symbolic analysis that can fully explain the emergence of the partially unstable attractors. To

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“…Many efforts for analyzing hyperchaotic dynamics have been reported in Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Chaotic and Hyperchaotic Dynamics of Smart Valves System Subject to a Sudden Contraction

Segala

Nataraj²

2016

Journal of Computational and Nonlinear Dynamics

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In this paper, we focus on determining the safe operational domain of a coupled actuator–valve configuration. The so-called “smart valves” system has increasingly been used in critical applications and missions including municipal piping networks, oil and gas fields, petrochemical plants, and more importantly, the U.S. Navy ships. A comprehensive dynamic analysis is hence needed to be carried out for capturing dangerous behaviors observed repeatedly in practice. Using some powerful tools of nonlinear dynamic analysis including Lyapunov exponents and Poincaré map, a comprehensive stability map is provided in order to determine the safe operational domain of the network in addition to characterizing the responses obtained. Coupled chaotic and hyperchaotic dynamics of two coupled solenoid-actuated butterfly valves are captured by running the network for some critical values through interconnected flow loads affected by the coupled actuators' variables. The significant effect of an unstable configuration of the valve–actuator on another set is thoroughly investigated to discuss the expected stability issues of a remote set due to others and vice versa.

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Chaos–hyperchaos transition in a class of models governed by Sommerfeld effect

Cited by 17 publications

References 35 publications

Sliding Mode Control and Geometrization Conjecture in Seismic Response

Sliding Mode Control and Geometrization Conjecture in Seismic Response

Partially unstable attractors in networks of forced integrate-and-fire oscillators

Chaotic and Hyperchaotic Dynamics of Smart Valves System Subject to a Sudden Contraction

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