Preference of attractors in noisy multistable systems

1999 ◽  
Vol 59 (5) ◽  
pp. 5253-5260 ◽  
Author(s):  
Suso Kraut ◽  
Ulrike Feudel ◽  
Celso Grebogi
Keyword(s):  
Multistable Systems

scholarly journals Counting statistics in multistable systems

2010 ◽  
Vol 81 (20) ◽  
Author(s):  
Gernot Schaller ◽  
Gerold Kießlich ◽  
Tobias Brandes
Keyword(s):  
Counting Statistics ◽  
Multistable Systems

scholarly journals Vortices Nucleation By Inherent Fluctuations In Nematic Liquid Crystal Cells

2021 ◽  
Author(s):  
Esteban Aguilera ◽  
Marcel G. Clerc ◽  
Valeska Zambra
Keyword(s):  
Liquid Crystal ◽  
Optical Tweezers ◽  
Nematic Liquid Crystal ◽  
Topological Defects ◽  
Optical Vortices ◽  
Topological Features ◽  
Nucleation Mechanisms ◽  
Multistable Systems ◽  
Light Beams ◽  
Crystal Cells

Abstract Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different states. In the case of these systems are described by vectorial fields, domains are connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. The interaction of light beams with matter vortices in liquid crystal cells is a natural source of optical vortices. The rhythms that govern the emergence of matter vortexes due to fluctuations are not established. Here we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a fair agreement with the theoretical findings.

scholarly journals Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
R. J. Escalante-González ◽  
Eric Campos
Keyword(s):  
Vector Field ◽  
Linear Systems ◽  
Piecewise Linear ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Key Space ◽  
Potential Applications ◽  
Current Design ◽  
Multistable Systems ◽  
Number Of Equilibria

In this work, we present an approach to design a multistable system with one-directional (1D), two-directional (2D), and three-directional (3D) hidden multiscroll attractor by defining a vector field on ℝ3 with an even number of equilibria. The design of multistable systems with hidden attractors remains a challenging task. Current design approaches are not as flexible as those that focus on self-excited attractors. To facilitate a design of hidden multiscroll attractors, we propose an approach that is based on the existence of self-excited double-scroll attractors and switching surfaces whose relationship with the local manifolds associated to the equilibria lead to the appearance of the hidden attractor. The multistable systems produced by the approach could be explored for potential applications in cryptography, since the number of attractors can be increased by design in multiple directions while preserving the hidden attractor allowing a bigger key space.

Non-Gaussian Noise Effects on Reliability of Multistable Systems

1995 ◽  
Vol 117 (3) ◽  
pp. 166-170 ◽  
Author(s):  
E. Simiu ◽  
M. Grigoriu
Keyword(s):  
Stochastic Systems ◽  
Necessary Condition ◽  
Deterministic Case ◽  
Limit States ◽  
Chaotic Motions ◽  
Stochastic Chaos ◽  
Stochastic Excitations ◽  
Safe Region ◽  
Multistable Systems ◽  
Non Gaussian

For certain types of compliant structures, the designer must consider limit states associated with the onset of fluidelastic instability. These limit states may include bifurcations from motion in a safe region of phase space to chaotic motion with exits (jumps) out of the safe region. In practice, such bifurcations occur in systems with noisy or stochastic excitations. For a wide class of dynamical systems, a fundamental connection between deterministic and stochastic chaos allows the application to stochastic systems of a necessary condition for the occurrence of chaos originally obtained by Melnikov for the deterministic case. We discuss the application of this condition to obtain probabilities that chaotic motions with jumps cannot occur in multistable systems excited by processes with tail-limited marginal distributions.

scholarly journals Basin stability approach for quantifying responses of multistable systems with parameters mismatch

Meccanica ◽  
2016 ◽  
Vol 51 (11) ◽  
pp. 2713-2726 ◽  
Author(s):  
P. Brzeski ◽  
M. Lazarek ◽  
T. Kapitaniak ◽  
J. Kurths ◽  
P. Perlikowski
Keyword(s):  
Multistable Systems ◽  
Basin Stability
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