Designing Hopf limit circle to dynamical systems via modified projective synchronization

Wen, Guilin

doi:10.1007/s11071-010-9810-7

Cited by 14 publications

(3 citation statements)

References 22 publications

(25 reference statements)

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“…Mainieri and Rehacek [9] first proposed the chaos projective synchronization scheme in 1999, but it was still very difficult to achieve projective synchronization between two or more chaotic nonlinear systems until Wen et al [10,11] presented an observer-based control scheme for projective chaos synchronization in 2004, whose prominent advantage is "no special limitation" for nonlinear dynamical systems to achieve projective chaos synchronization. Wen and co-authors also tried to explore the potential applications of projective synchronization to noise reduction in mechanical engineering [12,13], design bifurcation solutions [14,15] and so on.…”

Section: Introductionmentioning

confidence: 99%

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Xin

2015

Entropy

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A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.

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Section: Introductionmentioning

confidence: 99%

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Xin

2015

Entropy

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“…Various methods and techniques [3,4,5] have been developed, and many types of synchronization have been presented [9,10,12,13,14] and their main attention was focused on the synchronization in continuous-time systems. However, many models mathematics of physical process, chemical , biology and ecology are given by discrete dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

A new chaos synchronization criterion for discrete dynamical systems

Ouannas¹

2014

ams

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“…The research on periodic-impact stability and chaotic behavior has been further expanded to different types of vibratory systems with clearances or motion limiting constraints; see Refs. [3][4][5][6][7][8][9][10][11][12]. A special feature of vibro-impact systems is the so-called grazing effect, which leads to singularity of the impact Poincaré maps, i.e., the instability caused by low-velocity collisions.…”

Section: Introductionmentioning

confidence: 99%

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

et al. 2014

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A two-degree-of-freedom periodically forced system with a clearance is considered. The correlative relationship and matching law between dynamics and system parameters are analyzed by the co-simulation analysis of multi-parameter and multiperformance. Key parameters of the system, such as the exciting frequency, clearance value and constraint stiffness, are emphasized to analyze the influence of the main factors on its soft impact characteristics and reveal diversity, evolution and distribution regions of periodic-impact motions. The quantity of the fundamental group of p/1 impact motions, which have the excitation period and differ by the number p of impacts, is basically determined by the constraint stiffness. A series of grazing bifurcations occur with decreasing the exciting frequency so that the number p of impacts of the fundamental group of motions correspondingly increases one by one. As the constraint stiffness is very large, the impact number p of the fundamental group of motions becomes also big enough in low exciting frequency range. Consequently, the system possibly exhibits chattering-impact characteristics and the relative impact velocities successively attenuate in an excitation period. There exist a series of singular points between any two adjacent ones of the fundamental group of motions as the damping ratio or the damping constant of the viscous dashpot connecting two masses is very small, i.e., real-grazing and baregrazing bifurcation boundaries of one of them, saddlenode and period-doubling bifurcation boundaries of the other mutually cross themselves at the point of intersection and create two types of transition regions: hysteresis and tongue-shaped regions. A series of zones of regular and complex subharmonic impact motions are found to dominate in the tongue-shaped regions. The dimensionless parameters have been designed technically, under which large mass ratio or small supporting stiffness ratio leads to diversity and complexity of periodic-impact motions of the system. Based on the sampling ranges of parameters, the influence of system parameters on relative impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically studied.

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Designing Hopf limit circle to dynamical systems via modified projective synchronization

Cited by 14 publications

References 22 publications

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

A new chaos synchronization criterion for discrete dynamical systems

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

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