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[null,"1.","Record Nr.",null,"UNISA996490352803316"]
[null,null,"Autore",null,"Sun Kehui"]
[null,null,"Titolo",null,"Solution and characteristic analysis of fractional-order chaotic systems / / Kehui Sun, Shaobo He, Huihai Wang"]
[null,null,"Pubbl/distr/stampa",null,"Beijing, China ; ; Singapore : , : Science Press : , : Springer, , [2022]"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"981-19-3273-5"]
[null,null,"Descrizione fisica",null,"1 online resource (254 pages)"]
[null,null,"Disciplina",null,"515.83"]
[null,null,"Soggetti",null,"Fractional calculus"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Introduction -- Contents -- 1 Introduction -- 1.1 Overview of Chaos -- 1.1.1 The Origin and Development of Chaos -- 1.1.2 Definition of Chaos -- 1.1.3 Characteristics of Chaos -- 1.2 Overview of Fractional-Order Chaotic Systems -- 1.2.1 Definitions and Properties of Fractional Calculus -- 1.2.2 Overview of Solving Algorithms for Fractional-Order Chaotic Systems -- 1.3 Review on the Analysis Methods of Fractional-Order Chaotic Systems -- 1.3.1 Study on the Dynamical Behavior of Fractional-Order Chaotic Systems -- 1.3.2 Complexity of Fractional-Order Chaotic System and Its Definition -- 1.3.3 Complexity Analysis of Fractional-Order Chaotic Systems -- 1.4 Overview of the Application of Fractional Chaotic Systems -- 1.4.1 Circuit Implementation of Fractional-Order Chaotic Systems -- 1.4.2 Synchronization Control of Fractional-Order Chaotic Systems -- 1.4.3 Application of Fractional-Order Chaotic Systems in Secure Communication -- References -- 2 Frequency-Domain Approximation Method -- 2.1 Algorithm Principle -- 2.2 Dynamic Simulation -- 2.3 Algorithm Instance -- References -- 3 Predictor-Corrector Algorithm -- 3.1 Algorithm Description -- 3.2 Numerical Simulation -- 3.3 Algorithm Example: Dynamical Analysis of the Fractional-Order Simplified Lorenz Hyperchaotic System -- 3.3.1 Dynamics with the Variation of the System Order -- 3.3.2 Dynamics with the Variation of the Frequency ω -- References -- 4 Adomian Decomposition Method -- 4.1 Algorithm Description -- 4.2 Algorithm Example -- 4.2.1 Fractional-Order Lorenz Chaotic System -- 4.2.2 Fractional-Order Simplified Lorenz Chaos System -- 4.3 Adomian Decomposition Method for Fractional-Order Time-Delay Differential "]
[{"$nulls":4},"Equations -- References -- 5 Performance Comparison of Solution Algorithms -- 5.1 Uniqueness of Solutions of Fractional-Order Differential Equations."]
[{"$nulls":4},"5.2 Accuracy and Performance -- 5.3 Influence of Different Factors on the Minimum Order of Chaos -- 5.3.1 Minimum Order of Chaos with Different Algorithms -- 5.3.2 Simulation Step Size on the Minimum Order of Chaos -- 5.3.3 Lowest Order of Chaos with Different Derivative Orders -- 5.3.4 System Parameters on the Lowest Order of Chaos -- 5.3.5 The Optimal Minimum Order of Chaos -- References -- 6 Dynamics of Fractional-Order Chaotic Systems -- 6.1 Lyapunov Exponent Spectrum Calculation Algorithm -- 6.2 Dynamical Characterization of a Family of Fractional-Order Lorenz Systems -- 6.2.1 Fractional-Order Lorenz Chaotic System -- 6.2.2 Fractional-Order Simplified Lorenz Chaotic System -- 6.2.3 Fractional-Order Lorenz Hyperchaotic System -- 6.2.4 Fractional-Order Rössler Chaotic System -- 6.2.5 Fractional-Order Lorenz-Stenflo Chaotic System -- 6.2.6 Fractional-Order Simplified Lorenz Hyperchaotic System -- References -- 7 Complexity Analysis of Fractional-Order Chaotic System -- 7.1 Behavioral Complexity Algorithm -- 7.1.1 Research on Multivariate Permutation Entropy Algorithm -- 7.1.2 Complexity Analysis of Fractional-Order Chaotic Systems -- 7.1.3 Research on Improved Multi-Scale Permutation Entropy Algorithm -- 7.1.4 Complexity Analysis of Fractional-Order Chaotic System -- 7.2 Structural Complexity Algorithm -- 7.2.1 SE and C0 Complexity -- 7.2.2 Structural Complexity Analysis of Fractional-Order Chaotic System -- References -- 8 Circuit Design and Realization of Fractional-Order Chaotic System -- 8.1 Research on Analog Circuit of Fractional Chaos System -- 8.2 Design and Implementation of Fractional-Order Chaotic System on DSP -- 8.2.1 Algorithm for Solving Fractional-Order Simplified Lorenz System -- 8.2.2 Hardware Design of Fractional-Order Chaotic System -- 8.2.3 Software Design of Fractional Chaos System."]
[{"$nulls":4},"8.3 FPGA Design and Implementation of Fractional-Order Chaotic System -- 8.3.1 Design and Optimization of Circuit Structure -- 8.3.2 Design of Fractional Simplified Lorenz System Chaotic Signal Generator -- 8.3.3 Design of Floating-Point Arithmetic Units -- 8.3.4 Experimental Results and Analysis -- References -- 9 Applications of Fractional-Order Chaotic Systems in Secure Communications -- 9.1 Synchronous Control of the Fractional-Order Chaotic Systems -- 9.1.1 Coupled Synchronization of Fractional-Order Chaotic Systems -- 9.1.2 Generalized Function Projection Synchronization for Fractional-Order Chaotic Systems -- 9.1.3 Network Synchronization of Fractional-Order Chaotic Systems -- 9.2 Design of the Fractional-Order Chaotic Pseudo-Random Sequence Generator -- 9.2.1 Design of Chaotic Pseudo-Random Sequence Generator Based on the Fractional-Order Simplified Lorenz System -- 9.2.2 Performance Tests for Chaotic Pseudo-Random Sequences -- 9.2.3 Design of the Fractional-Order Lorenz Hyperchaotic Pseudo-Random Sequence Generator -- 9.3 Study of Fractional-Order Chaotic Image Encryption Algorithm -- 9.3.1 Image Encryption Algorithm Based on Fractional-Order Hyperchaotic System -- 9.3.2 Security Analysis of Image Encryption Algorithm -- 9.4 Fractional-Order Chaotic Spread Spectrum Communication Systems -- 9.4.1 Spread Spectrum Codes in Spread Spectrum Communication Systems -- 9.4.2 Design of a Single-User Fractional-Order Chaotic Spread Spectrum Communication System Based on Correlated Reception -- 9.4.3 Performance Analysis of the Spread Spectrum Communication Systems -- 9.4.4 Design of a Multi-user Chaotic Spread Spectrum Communication System Based on Correlated Reception -- 9.4.5 Design of a Multi-User Chaotic Spread Spectrum Communication System Based "]
[{"$nulls":4},"on the Rake Reception -- References."]
[{"$nulls":4},"10 Solution and Characteristic Analysis of Fractional-Order Discrete Chaotic System -- 10.1 Research Progress of Fractional-Order Discrete Chaotic Systems -- 10.2 Definition of Discrete Fractional-Order Difference -- 10.3 Characteristic Analysis of Fractional-Order Discrete Chaotic System -- 10.3.1 The Fractional-Order Logistic Map -- 10.3.2 The Fractional-Order Hénon Map -- 10.3.3 The Fractional-Order High-Dimensional Chaotic Map -- References -- Appendix Program Code -- Reference."]