Dynamics with chaos and fractals. (2020)

• Record Type: Book
• Further Information: Note: Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily.
• Other Names: Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad
• Contents: Intro -- Preface -- Contents -- 1 Introduction -- References -- 2 The Unpredictable Point and Poincaré Chaos -- 2.1 Preliminaries -- 2.2 Dynamics with Unpredictable Points -- 2.3 Chaos on the Quasi-Minimal Set -- 2.4 Applications -- 2.5 Notes -- References -- 3 Unpredictability in Bebutov Dynamics -- 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Unpredictable Functions -- 3.4 Unpredictable Solutions of Quasilinear Systems -- 3.5 Examples -- 3.6 Notes -- References -- 4 Nonlinear Unpredictable Perturbations -- 4.1 Preliminaries -- 4.2 An Unpredictable Sequence of the Symbolic Dynamics 4.3 An Unpredictable Solution of the Logistic Map -- 4.4 An Unpredictable Function -- 4.5 Unpredictable Solutions of Differential Equations -- 4.6 Notes -- References -- 5 Unpredictability in Topological Dynamics -- 5.1 Introduction -- 5.2 Quasilinear Delay Differential Equations -- 5.3 Quasilinear Discrete Equations -- 5.4 A Continuous Unpredictable Function via the Logistic Map -- 5.5 Examples -- 5.6 A Hopfield Neural Network -- 5.7 Notes -- References -- 6 Unpredictable Solutions of Hyperbolic Linear Equations -- 6.1 Preliminaries -- 6.2 Differential Equations with Unpredictable Solutions 6.3 Discrete Equations with Unpredictable Solutions -- 6.4 Examples -- References -- 7 Strongly Unpredictable Solutions -- 7.1 Preliminaries -- 7.2 Main Results -- 7.3 Examples -- References -- 8 Li-Yorke Chaos in Hybrid Systems on a Time Scale -- 8.1 Introduction -- 8.2 Preliminaries -- 8.3 Bounded Solutions -- 8.4 The Chaotic Dynamics -- 8.5 An Example -- 8.6 Notes -- References -- 9 Homoclinic and Heteroclinic Motions in Economic Models -- 9.1 Introduction -- 9.2 The Model -- 9.3 Homoclinic and Heteroclinic Motions -- 9.4 An Example -- 9.5 Notes -- References 10 Global Weather and Climate in the Light of El Niño-Southern Oscillation -- 10.1 Introduction and Preliminaries -- 10.1.1 Unpredictability of Weather and Deterministic Chaos -- 10.1.2 Ocean-Atmosphere Interaction and Its Effects on Global Weather -- 10.1.3 El Niño Chaotic Dynamics -- 10.1.4 Sea Surface Temperature Advection Equation -- 10.1.5 Unpredictability and Poincaré Chaos -- 10.1.6 The Role of Chaos in Global Weather and Climate -- 10.2 Unpredictable Solution of the Advection Equation -- 10.2.1 Unpredictability Due to the Forcing Source Term 10.2.2 Unpredictability Due to the Current Velocity -- 10.3 Chaotic Dynamics of the Global Ocean Parameters -- 10.3.1 Extension of Chaos in Coupled Advection Equations -- 10.3.2 Coupling of the Advection Equation with VallisModel -- 10.3.3 Coupling of Vallis Models -- 10.4 Ocean-Atmosphere Unpredictability Interaction -- 10.5 Notes -- References -- 11 Fractals: Dynamics in the Geometry -- 11.1 Introduction -- 11.2 Fatou-Julia Iteration -- 11.3 How to Map Fractals -- 11.4 Dynamics for Julia Sets -- 11.4.1 Discrete Dynamics -- 11.4.2 Continuous Dynamics
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (233 pages)
• Subjects: 003/.857; Chaotic behavior in systems; Fractals; Chaotic behavior in systems; Fractals; Electronic books
• Languages: English
• ISBNs: 9783030358549; 3030358542
• Related ISBNs: 9783030358532; 3030358534
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.