scholarly journals Classical infinite-range-interaction Heisenberg ferromagnetic model:   Metastability and sensitivity to initial conditions

2003 ◽  
Vol 68 (3) ◽  
Author(s):  
Fernando D. Nobre ◽  
Constantino Tsallis
Keyword(s):  
Initial Conditions ◽  
Range Interaction ◽  
Sensitivity To Initial Conditions ◽  
Infinite Range

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

2020 ◽  
Vol 18 (1) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Map ◽  
Security Applications ◽  
The Common ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Sensitivity To Initial Conditions ◽  
Diffusion Properties

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

scholarly journals Direct Scaling Analysis of Fermionic Multiparticle Correlated Anderson Models with Infinite-Range Interaction

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Victor Chulaevsky
Keyword(s):  
Dynamical Localization ◽  
Scaling Analysis ◽  
Range Interaction ◽  
Direct Scaling ◽  
Strongly Mixing ◽  
Optimal Decay ◽  
Decay Bounds ◽  
Multiparticle Systems ◽  
Infinite Range ◽  
Anderson Models

We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs. Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials. Earlier results required the random potential to be IID.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

Boundedness and Other Theories for Complex Systems

2013 ◽  
pp. 108-125
Keyword(s):  
Initial Conditions ◽  
Traditional Approach ◽  
Deterministic Chaos ◽  
Mathematical Object ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Universal Properties ◽  
The One ◽  
Global Invariant ◽  
Sensitivity To Initial Conditions

A comparison between the concept of boundedness on the one hand, and the theory of self-organized criticality (SOC) and the deterministic chaos on the other hand, is made. The focus is put on the methodological importance of the general frame through which an enormous class of empirical observations is viewed. The major difference between the concept of boundedness and the theory of self organized criticality is that under boundedness, the response comprises both specific and universal part, and thus a system has well defined “identity,” while SOC assumes response as a global invariant which has only universal properties. Unlike the deterministic chaos, the boundedness is free to explain the sensitivity to initial conditions independently from the mathematical object that generates them. Alongside, it turns out that the traditional approach to the deterministic chaos has its ample understanding under the concept of boundedness.

scholarly journals Rotational Behavior of Cometary-type Bodies

1992 ◽  
Vol 152 ◽  
pp. 291-296
Author(s):  
Eric Bois ◽  
Pascal Oberti ◽  
Claude Froeschlé
Keyword(s):  
Qualitative Study ◽  
Rotational Motion ◽  
Numerical Experiments ◽  
Initial Conditions ◽  
Close Approach ◽  
Rotational Behavior ◽  
Comet Nucleus ◽  
Gravitational Perturbation ◽  
The Sun ◽  
Sensitivity To Initial Conditions

The present paper deals with a general dynamical qualitative study of the rotational motion for cometary-type bodies submitted to gravitational torques. Numerical experiments of the evolution of comet nucleus attitude have been then performed, including the Sun and Jupiter's disturbing torques in the model. Results show small effects of the solar gravitational perturbation for Halley-type orbits. Only a very close-approach with Jupiter induces notable effects. The latter configuration presents some interesting sensitivity to initial conditions.

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