Results 251 to 260 of about 12,183,826 (272)

Synchronization of Chaotic Fractional Chen System

Journal of the Physical Society of Japan, 2005
The complete synchronization of two coupled Chen's systems with fractional derivatives is studied. The driven Chen's system has the form \[ \frac{d^{q_1}x_m}{dt^{q_1}} = a(y_m-x_m), \] \[ \frac{d^{q_2}y_m}{dt^{q_2}} = (c-a)x_m -x_m z_m +c y_m, \] \[ \frac{d^{q_3}z_m}{dt^{q_3}} = x_m y_m -b z_m, \] the response system reads \[ \frac{d^{q_1}x_s}{dt^{q_1}}
Deng, Weihua, Li, Changpin
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BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM

International Journal of Bifurcation and Chaos, 2002
This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter.
Jinhu Lu 0001, Guanrong Chen, Daizhan Cheng, Sergej Celikovský   +3 more
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Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013
In this paper, we show, by means of a linear scaling in time and coordinates, that the Chen system, given by x=a(y-x), y=(c-a)x+cy-xz, ż=-bz+xy, is, generically (c≠0), a special case of the Lorenz system. First, we infer that it is enough to consider two parameters to study its dynamics.
Algaba, Antonio, Fernández-Sánchez, Fernando, Merino, Manuel, Rodríguez-Luis, Alejandro J.   +3 more
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DARBOUX POLYNOMIALS AND ALGEBRAIC INTEGRABILITY OF THE CHEN SYSTEM

International Journal of Bifurcation and Chaos, 2007
In this paper, we characterize all the Darboux polynomials of the Chen system, [Formula: see text], and prove that the system is not algebraic integrability. For proving the results, we use the weight homogeneous polynomials and the method of characteristics.
Tinghua Lü, Xiang Zhang
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New Topological Horseshoe in the Chen System

International Journal of Bifurcation and Chaos
In this paper, we explore the rich dynamics in the Chen system using Runge–Kutta method and Deep Neural Networks (DNNs). Compared with the Lorenz system, we find that the first return map [Formula: see text] of the Chen system exhibits a more complex structure of continuous regions in the Poincaré section.
Junfeng Cheng, Xiao-Song Yang
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Complex Dynamical Behaviors of the Chaotic Chen's System

International Journal of Bifurcation and Chaos, 2003
In this paper, the complex dynamical behaviors of the chaotic trajectories of Chen's system are analyzed in detail, with its precise bound derived for the first time. In particular, it is rigorously proved that all nontrivial trajectories of the system always travel alternatively through two specific Poincaré projections for infinitely many times.
Tianshou Zhou, Yun Tang, Guanrong Chen
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THE CHEN SYSTEM HAVING AN INVARIANT ALGEBRAIC SURFACE

International Journal of Bifurcation and Chaos, 2008
In this paper, we characterize the dynamics of the Chen system ẋ = a(y - x), ẏ = (c - a)x - xz + cy, ż = xy - bz which has an invariant algebraic surface.
Jinlong Cao, Cheng Chen, Xiang Zhang
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Bifurcation and Dynamics of the complex Chen systems

Discrete and Continuous Dynamical Systems - B
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Lina, Zhang, Xu
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A Geometric Approach of the Chen's System

IFAC Proceedings Volumes, 2012
Abstract The chaotic systems have been studied starting from the early 1960s by the help of Lorenz system. Since then, other chaotic attractors, such as the Chua's system, the Lu's system and so on, have been developed. In 1999, based on an engineering feed-back anti-control approach, Chen provided a new system (see Chen (1999) for details).
Camelia Pop Ariesanu, Camelia Petrisor
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Dynamical Pattern Classification of Lorenz System and Chen System

2008
Recently, an approach for rapid dynamical pattern recognition was proposed, by which a dynamical pattern can be locally accurately identified and rapidly recognized using localized radial basis function (RBF) networks. Further, a scheme for classification of dynamical patterns was presented.
Hao Cheng, Cong Wang 0007
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