Piece-wise and max-type difference equations : periodic and eventually periodic solutions /: periodic and eventually periodic solutions. (2020)

• Record Type: Book
• Further Information: Note: Michael A. Radin.
• Authors: Radin, Michael A (Michael Alexander)
• Contents: Contents Preface vii Acknowledgments ix Author xi Introduction 1 1.1 Recursive Sequences . . . . . . . . . . . . . . . . . . . . . . . 3 Order and Explicit Solution of a ∆.E. . . . . . . . . . . . . . 5 Non-Autonomous Difference Equations . . . . . . . . . . . . 6 1.4 Periodic Sequences . . . . . . . . . . . . . . . . . . . . . . . . 7 Alternating Periodic Cycles . . . . . . . . . . . . . . . . . . . 12 Specific Patterns of Periodic Cycles . . . . . . . . . . . . . . 13 Eventually Periodic Sequences . . . . . . . . . . . . . . . . . 14 1.8 Piece-wise Sequences . . . . . . . . . . . . . . . . . . . . . . 18 1.9 Chapter 1 Exercises . . . . . . . . . . . . . . . . . . . . . . . 20 Linear Difference Equations 25 Autonomous Linear Difference Equations . . . . . . . . . . . 26 2.2 Non-Autonomous Linear ∆.E. ’s . . . . . . . . . . . . . . . . 27 2.2.1 Multiplicative Form of Eq. (2.5) . . . . . . . . . . . . . 27 2.2.2 Additive Form of Eq. (2.5) . . . . . . . . . . . . . . . . 31 2.3 Chapter 2 Exercises . . . . . . . . . . . . . . . . . . . . . . . 40 Riccati Difference Equations 43 3.1 First-Order Riccati ∆.E. . . . . . . . . . . . . . . . . . . . . 43 3.2 Second-Order Riccati ∆.E. . . . . . . . . . . . . . . . . . . . 50 3.3 Chapter 3 Exercises . . . . . . . . . . . . . . . . . . . . . . . 60 Piece-wise Difference Equations 63 4.1 The Collatz Conjectures . . . . . . . . . . . . . . . . . . . . 64 4.2 The Tent-Map . . . . . . . . . . . . . . . . . . . . . . . . . . 65 The Autonomous Neuron Model . . . . . . . . . . . . . . . . 72 Autonomous Neuron Model when β = 1 . . . . . . . . 79 Non-Autonomous Neuron Model . . . . . . . . . . . . . . . . 82 Non-Autonomous Neuron Model when β 0β 1 = 1 . . . 88 4.5 The Williamson Model . . . . . . . . . . . . . . . . . . . . . 92 4.6 The West Nile Epidemics Model . . . . . . . . . . . . . . . . 93 4.7 Chapter 4 Exercises . . . . . . . . . . . . . . . . . . . . . . . 93 5 Max-Type Difference Equations 97 5.1 The Autonomous Case (Eq. [5.1]) . . . . . . . . . . . . . . . 97 Eventually Periodic with Period-2 . . . . . . . . . . . 100 Eventually Periodic with Period-4 . . . . . . . . . . . 109 Eventually Periodic with Period-3 . . . . . . . . . . . 117 Eventually Constant with K = 1 . . . . . . . . . . . . 125 5.2 The Non-Autonomous Case (Eq. [5.2]) . . . . . . . . . . . . . 130 Eventually Periodic with Period-2 . . . . . . . . . . . 132 Eventually Periodic with Period-4 . . . . . . . . . . . 140 Eventually Periodic with Period-6 . . . . . . . . . . . 144 5.3 Chapter 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . 147 6 Appendices 149 6.1 Patterns of Sequences . . . . . . . . . . . . . . . . . . . . . . 149 6.2 Alternating Patterns of Sequences . . . . . . . . . . . . . . . 149 6.3 Finite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Convergent Infinite Series . . . . . . . . . . . . . . . . . . . . 150 Periodicity and Modulo Arithmetic . . . . . . . . . . . . . . 151 Alternating Periodicity . . . . . . . . . . . . . . . . . . 151 Patterns as an Initial Value Problem . . . . . . . . . . . . . 152 Specific Periodic Patterns . . . . . . . . . . . . . . . . . . . . 153 Bibliography 155 Index 157
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2020
• Extent: 1 online resource, illustrations (colour)
• Subjects: 515.625; Difference equations
• Languages: English
• ISBNs: 9780429855252; 9780429855269; 9780429855245; 9780429457616
• Related ISBNs: 9781138313507
• Notes: Note: Description based on CIP data; resource not viewed.
• 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.