scholarly journals On the optimality of double-bracket flows

2004 ◽  
Vol 2004 (62) ◽  
pp. 3301-3319 ◽  
Author(s):  
Anthony M. Bloch ◽  
Arieh Iserles
Keyword(s):  
Fixed Point ◽  
Global Optimality ◽  
Stable Fixed Point ◽  
Different Types

We analyze the optimality of the stable fixed point of the double-bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schattenp-norms.

Three Types of Chaotic Attractors in 3 D Maps

1993 ◽  
Vol 48 (5-6) ◽  
pp. 666-668 ◽  
Author(s):  
Michael Klein ◽  
Achim Kittel ◽  
Gerold Baier
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Three Dimensions ◽  
Chaotic Attractors ◽  
Stable Fixed Point ◽  
Fractal Structures ◽  
One Dimensional ◽  
Different Types

Abstract Coupling a one-dimensional chaotic forcing to a stable fixed point in the plane may generate different fractal attractors embedded in three dimensions. The system with real eigenvalues of the fixed point gives rise to simple chaotic attractors with three different types of fractal structures. We show that the competition of local exponents provides a generic criterion for the classification of the fractal structures in dynamical systems.

Estimation of the Stable Fixed Point of Passive Dynamic Walking with BP Neural Network

ROBOT ◽  
2010 ◽  
Vol 32 (4) ◽  
pp. 478-483 ◽  
Author(s):  
Xiuhua NI ◽  
Weishan CHEN ◽  
Junkao LIU ◽  
Shengjun SHI
Keyword(s):  
Neural Network ◽  
Fixed Point ◽  
Bp Neural Network ◽  
Stable Fixed Point ◽  
Dynamic Walking ◽  
Passive Dynamic Walking

scholarly journals THE CASE OF ASYMPTOTIC SUPERSYMMETRY

2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Coupling ◽  
High Energy ◽  
Systematic Investigation ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Asymptotic State ◽  
Stable Fixed Point ◽  
Scalar Couplings

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Parameter Space ◽  
Landau Theory ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Theory Analysis ◽  
Continuous Transition ◽  
Dimensional Parameter ◽  
First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

scholarly journals Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps

2018 ◽  
Vol 28 (04) ◽  
pp. 1830011
Author(s):  
Mio Kobayashi ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Chaotic Behavior ◽  
Periodic Points ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Bifurcation Structure ◽  
Unstable Fixed Point ◽  
Gaussian Map ◽  
Gaussian Maps

A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the [Formula: see text]-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

scholarly journals DYNAMICS OF DELAY-COUPLED EXCITABLE NEURAL SYSTEMS

2009 ◽  
Vol 19 (02) ◽  
pp. 745-753 ◽  
Author(s):  
M. A. DAHLEM ◽  
G. HILLER ◽  
A. PANCHUK ◽  
E. SCHÖLL
Keyword(s):  
Nonlinear Dynamics ◽  
Fixed Point ◽  
Limit Cycles ◽  
Coupling Strength ◽  
Neural Systems ◽  
Stable Fixed Point ◽  
Bifurcation Of Limit Cycles ◽  
Large Delay ◽  
Saddle Node Bifurcation ◽  
Delay Times

We study the nonlinear dynamics of two delay-coupled neural systems each modeled by excitable dynamics of FitzHugh–Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for sufficiently large delay times τ and coupling strength C. As the mechanism for these delay-induced oscillations, we identify a saddle-node bifurcation of limit cycles.

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