Chaos synchronization in fractional differential systems

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1999 • 20,349 citations

Synchronization in chaotic systems

1990 • 10,223 citations

Fractional Integrals and Derivatives: Theory and Applications

1993 • 7,719 citations

Synchronization: A Universal Concept in Nonlinear Sciences

2001 • 5,925 citations

Synchronization

2001 • 4,245 citations

Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers

1999 • 2,887 citations

The synchronization of chaotic systems

2002 • 2,570 citations

Untitled

2002 • 1,876 citations

Recent history of fractional calculus

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Stability results for fractional differential equations with applications to control processing

1996 • 1,386 citations

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

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General Approach for Chaotic Synchronization with Applications to Communication

1995 • 1,001 citations

Stability analysis of linear fractional differential system with multiple time delays

2006 • 855 citations

Projective Synchronization In Three-Dimensional Chaotic Systems

1999 • 771 citations

Chaos in a fractional order Chua's system

1995 • 743 citations

Fractional order state equations for the control of viscoelasticallydamped structures

1991 • 732 citations

Chaotic Dynamics of the Fractional Lorenz System

2003 • 725 citations

On-off intermittency: A mechanism for bursting

1993 • 685 citations

Chaos and hyperchaos in the fractional-order Rössler equations

2004 • 644 citations

Remarks on fractional derivatives

2006 • 636 citations

Generalized synchronization of chaos: The auxiliary system approach

1996 • 631 citations

Chaos in Chen's system with a fractional order

2004 • 519 citations

Bubbling of attractors and synchronisation of chaotic oscillators

1994 • 481 citations

Blowout bifurcations: the occurrence of riddled basins and on-off intermittency

1994 • 476 citations

RIDDLED BASINS

1992 • 385 citations

Chaos synchronization of the fractional Lü system

2005 • 376 citations

Chaotic dynamics of the fractional-order Lü system and its synchronization

2006 • 341 citations

On Riemann-Liouville and Caputo Derivatives

2011 • 315 citations

Quantum Lévy Processes and Fractional Kinetics

1999 • 281 citations

Weak and strong synchronization of chaos

1996 • 281 citations

Synchronization of chaotic fractional-order systems via active sliding mode controller

2007 • 256 citations

Chaotic dynamics and synchronization of fractional-order Arneodo’s systems

2005 • 252 citations

Numerical approaches to fractional calculus and fractional ordinary differential equation

2011 • 233 citations

Chaos synchronization of the Chua system with a fractional order

2005 • 226 citations

Experimental and Numerical Evidence for Riddled Basins in Coupled Chaotic Systems

1994 • 221 citations

Electromagnetic Theory

2011 • 215 citations

Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves

1991 • 206 citations

Projective synchronization of fractional order chaotic system based on linear separation

2007 • 204 citations

Dynamic analysis of the fractional-order Liu system and its synchronization

2007 • 199 citations

Transition to chaos for random dynamical systems

1990 • 197 citations

Chaos, feedback control and synchronization of a fractional-order modified Autonomous Van der Pol–Duffing circuit

2010 • 176 citations

Chaos in the fractional order unified system and its synchronization

2007 • 176 citations

Distributed-Order Dynamic Systems

2012 • 166 citations

Synchronization of fractional order chaotic systems

2003 • 163 citations

A simple global synchronization criterion for coupled chaotic systems

2003 • 163 citations

Scaling behavior of chaotic systems with riddled basins

1993 • 157 citations

Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems

2007 • 152 citations

Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

2009 • 151 citations

Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order

2007 • 148 citations

Function projective synchronization for fractional-order chaotic systems

2010 • 129 citations

On chaos synchronization of fractional differential equations

2006 • 122 citations

SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL

2010 • 117 citations

A speech encryption using fractional chaotic systems

2010 • 117 citations

Numerical algorithm based on Adomian decomposition for fractional differential equations

2009 • 115 citations

Synchronization in fractional-order differential systems

2005 • 114 citations

Synchronization of a new fractional-order hyperchaotic system

2009 • 111 citations

Chaos and synchronization of the fractional-order Chua’s system

2007 • 101 citations

Generalized projective synchronization of the fractional-order Chen hyperchaotic system

2008 • 100 citations

Synchronization of Chaotic Fractional Chen System

2005 • 95 citations

Synchronization of fractional order chaotic systems

2006 • 93 citations

Generalized projective synchronization of fractional order chaotic systems

2008 • 85 citations

Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal

2006 • 84 citations

Hybrid projective synchronization of chaotic fractional order systems with different dimensions

2010 • 83 citations

Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor

2006 • 79 citations

CHAOS SYNCHRONIZATION OF FRACTIONAL-ORDER DIFFERENTIAL SYSTEMS

2006 • 78 citations

Robust synchronization of perturbed Chen’s fractional-order chaotic systems

2010 • 77 citations

Chaos synchronization of the fractional-order Chen’s system

2008 • 71 citations

The synchronization of fractional-order Rössler hyperchaotic systems

2007 • 69 citations

Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control

2009 • 68 citations

Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems

2010 • 68 citations

On the bound of the Lyapunov exponents for the fractional differential systems

2010 • 66 citations

Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?

2006 • 62 citations

A new chaotic system with fractional order and its projective synchronization

2010 • 62 citations

Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization

2006 • 61 citations

Introduction to fractional integrability and differentiability

2011 • 61 citations

Locally and globally riddled basins in two coupled piecewise-linear maps

1997 • 58 citations

Hybrid projective synchronization in a chaotic complex nonlinear system

2008 • 57 citations

Estimating the Lyapunov exponents of discrete systems

2004 • 55 citations

Synchronization of two coupled fractional-order chaotic oscillators

2005 • 54 citations

CHAOS AT SCHOOL: CHUA'S CIRCUIT FOR STUDENTS IN JUNIOR AND SENIOR HIGH SCHOOL

2010 • 54 citations

CALCULATION OF BIFURCATION CURVES BY MAP REPLACEMENT

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On-off intermittency in an experimental synchronization process

1995 • 53 citations

Transform Methods with Applications to Engineering and Operations Research

1978 • 53 citations

Generalized synchronization in fractional order systems

2007 • 53 citations

Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

2008 • 47 citations

Loss of synchronization in coupled Rössler systems

2001 • 41 citations

Synchronization in coupled nonidentical incommensurate fractional-order systems

2009 • 39 citations

Projective synchronization in coupled fractional order chaotic Rossler system and its control

2007 • 37 citations

Chaos Synchronization between Two Different Fractional Systems of Lorenz Family

2009 • 37 citations

Outer synchronization between two different fractional-order general complex dynamical networks

2010 • 36 citations

Analysis of a fractional order Van der Pol-like oscillator via describing function method

2010 • 33 citations

Controlling general projective synchronization of fractional order Rossler systems

2007 • 27 citations

Complicated basins in external-cavity semiconductor lasers

2003 • 27 citations

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

2010 • 23 citations

Projective Synchronization in Fractional Order Chaotic Systems and Its Control

2006 • 22 citations

Chaotic synchronization for a class of fractional-order chaotic systems

2007 • 20 citations

Chaotic Synchronization between Coupled Pancreatic β-Cells

2000 • 19 citations

Chaotic synchronization of a fractional neuron network system with time-varying delays

2009 • 17 citations

Conclusions and Comments

1985 • 15 citations

Transcritical riddling in a system of coupled maps

2001 • 14 citations

Experimental observation of riddled behaviour (electronic system)

1995 • 14 citations

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

2010 • 14 citations

Construction of a New Fractional Chaotic System and Generalized Synchronization

2010 • 13 citations

Experimental evidence of locally intermingled basins of attraction in coupled Chua's circuits

1997 • 12 citations

Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems

2006 • 10 citations

Generalized Synchronization Between Different Fractional-Order Chaotic Systems

2008 • 9 citations

Synchronization of Fractional-Order Chaotic System via Adaptive PID Controller

2009 • 9 citations

Generalized Synchronization Between Different Fractional-Order Chaotic Systems

2008 • 8 citations

SYNCHRONIZATION OF LIMIT SETS

2007 • 3 citations

Anticipating synchronization of the fractional-order system via nonlinear observer

2009 • 2 citations