Chaotic dynamics in a class of three dimensional Glass networks

2006 ◽  
Vol 16 (3) ◽  
pp. 033101 ◽  
Author(s):  
Qingdu Li ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Three Dimensional

scholarly journals A Study in Three-Dimensional Chaotic Dynamics: Granular Flow and Transport in a Bi-Axial Spherical Tumbler

2014 ◽  
Vol 13 (2) ◽  
pp. 901-943 ◽  
Author(s):  
Ivan C. Christov ◽  
Richard M. Lueptow ◽  
Julio M. Ottino ◽  
Rob Sturman
Keyword(s):  
Granular Flow ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Flow And Transport

scholarly journals Chaotic Dynamics of a Three-dimensional Endomorphism

2019 ◽  
Vol 12 (1) ◽  
pp. 36-50
Author(s):  
Akroune Nourredine ◽  
◽  
Gharout Hacene ◽  
Prunaret Daniele-Fournier ◽  
Taha Abelkadous ◽  
...  
Keyword(s):  
Chaotic Dynamics ◽  
Three Dimensional

Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Nataliya V. Stankevich ◽  
Natalya A. Shchegoleva ◽  
Igor R. Sataev ◽  
Alexander P. Kuznetsov
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Parameter Plane ◽  
Poincare Section ◽  
Dimensional Torus ◽  
Typical Structure ◽  
Periodic Oscillations ◽  
Torus Breakdown ◽  
Periodic Dynamics

Abstract Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincaré section, we have shown destruction of three-frequency torus.

A New Class of Three-Dimensional Maps with Hidden Chaotic Dynamics

2016 ◽  
Vol 26 (12) ◽  
pp. 1650206 ◽  
Author(s):  
Haibo Jiang ◽  
Yang Liu ◽  
Zhouchao Wei ◽  
Liping Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Basins Of Attraction ◽  
Chaotic Attractors ◽  
Computer Search ◽  
New Class ◽  
Special Concern

This paper studies a new class of three-dimensional maps in a Jerk-like structure with a special concern of their hidden chaotic dynamics. Our investigation focuses on the hidden chaotic attractors in three typical scenarios of fixed points, namely no fixed point, single fixed point, and two fixed points. A systematic computer search is performed to explore possible hidden chaotic attractors, and a number of examples of the proposed maps are used for demonstration. Numerical results show that the routes to hidden chaotic attractors are complex, and the basins of attraction for the hidden chaotic attractors could be tiny, so that using the standard computational procedure for localization is impossible.

THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS

2005 ◽  
Vol 15 (11) ◽  
pp. 3493-3508 ◽  
Author(s):  
S. V. GONCHENKO ◽  
I. I. OVSYANNIKOV ◽  
C. SIMÓ ◽  
D. TURAEV
Keyword(s):  
Lyapunov Exponent ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Maximal Lyapunov Exponent ◽  
Hénon Map ◽  
Henon Map ◽  
Quadratic Map ◽  
Different Types ◽  
Natural Way

We discuss a rather new phenomenon in chaotic dynamics connected with the fact that some three-dimensional diffeomorphisms can possess wild Lorenz-type strange attractors. These attractors persist for open domains in the parameter space. In particular, we report on the existence of such domains for a three-dimensional Hénon map (a simple quadratic map with a constant Jacobian which occurs in a natural way in unfoldings of several types of homoclinic bifurcations). Among other observations, we have evidence that there are different types of Lorenz-like attractor domains in the parameter space of the 3D Hénon map. In all cases the maximal Lyapunov exponent, Λ1, is positive. Concerning the next Lyapunov exponent, Λ2, there are open domains where it is definitely positive, others where it is definitely negative and, finally, domains where it cannot be distinguished numerically from zero (i.e. |Λ2| < ρ, where ρ is some tolerance ranging between 10-5 and 10-6). Furthermore, several other types of interesting attractors have been found in this family of 3D Hénon maps.

scholarly journals A nonlinear macrodynamic model with fixed exchange rates: Its dynamics and noise effects

2000 ◽  
Vol 4 (4) ◽  
pp. 319-331 ◽  
Author(s):  
Toichiro Asada ◽  
Toichio Inaba ◽  
Tetsuya Misawa
Keyword(s):  
Exchange Rates ◽  
Open Economy ◽  
Chaotic Dynamics ◽  
Small Open Economy ◽  
Three Dimensional ◽  
Basic Structure ◽  
Stochastic Disturbances ◽  
Noise Effects ◽  
Fixed Exchange Rates ◽  
Linear Approximation Method

In this paper, we formulate a discrete time version of the Kaldorian macrodynamic model in a small open economy with fixed exchange rates. The model is described by a system of the three-dimensional nonlinear difference equations with and without stochastic disturbances (noise effects). We study the local stability/instability properties analytically by using the linear approximation method, and chaotic dynamics with and without noise effects are investigated by means of numerical simulations. In general, it is believed that the effect of the noise is to obscure the basic structure of the system. But, this is not necessarily the case. We show by means of numerical analysis that the noise can reveal the hidden structure of the model contrary to the usual intuition in some situations.

scholarly journals Chaotic dynamics in a flexible exchange rate system:A study of noise effects

2000 ◽  
Vol 4 (4) ◽  
pp. 309-317 ◽  
Author(s):  
Toichiro Asada ◽  
Tetsuya Misawa ◽  
Toshio Inaba
Keyword(s):  
Exchange Rate ◽  
Foreign Exchange ◽  
Open Economy ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Flexible Exchange Rate ◽  
Foreign Exchange Rate ◽  
Cycle Model ◽  
Goods Market ◽  
Business Cycle Model

In this paper, we investigate by means of analytical method and numerical simulations the properties of three-dimensional business cycle model, in which foreign exchange rate is flexible and a parameter is fluctuated by noise. The model is a discrete time version of Asada (Journal of Economics, 62, 239–269,1995)'s continuous time open economy model without noise. We show (1) noise may suppress the burst of flexible foreign exchange rate when its behavior begins to burst as a bifurcation parameter (adjustment speed of the goods market) is increased, (2) the windows of cycles can be broken by noise, and (3) noise may reveal the hidden structures.

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