Piece wise and Max type difference equations periodic and eventually periodic solutions 1st Edition by Michael Radin ISBN 9780429855252 0429855257

1 Introduction

1.1 Recursive Sequences

1.2 Order and Explicit Solution of a Δ.E.

1.3 Non-Autonomous Difference Equations

1.4 Periodic Sequences

1.5 Alternating Periodic Cycles

1.6 Specific Patterns of Periodic Cycles

1.7 Eventually Periodic Sequences

1.8 Piece-wise Sequences

1.9 Chapter 1 Exercises

2 Linear Difference Equations

2.1 Autonomous Linear Difference Equations

2.2 Non-Autonomous Linear Δ.E.’s

2.2.1 Multiplicative Form of Eq. (2.5)

2.2.2 Additive Form of Eq. (2.5)

2.3 Chapter 2 Exercises

3 Riccati Difference Equations

3.1 First-Order Riccati Δ.E.

3.2 Second-Order Riccati Δ.E.

3.3 Chapter 3 Exercises

4 Piece-wise Difference Equations

4.1 The Collatz Conjectures

4.2 The Tent-Map

4.3 The Autonomous Neuron Model

4.3.1 Autonomous Neuron Model when β = 1

4.4 Non-Autonomous Neuron Model

4.4.1 Non-Autonomous Neuron Model when β0β1 = 1

4.5 The Williamson Model

4.6 The West Nile Epidemics Model

4.7 Chapter 4 Exercises

5 Max-Type Difference Equations

5.1 The Autonomous Case (Eq. [5.1])

5.1.1 Eventually Periodic with Period-2

5.1.2 Eventually Periodic with Period-4

5.1.3 Eventually Periodic with Period-3

5.1.4 Eventually Constant with K = 1

5.2 The Non-Autonomous Case (Eq. [5.2])

5.2.1 Eventually Periodic with Period-2

5.2.2 Eventually Periodic with Period-4

5.2.3 Eventually Periodic with Period-6

5.3 Chapter 5 Exercises

6 Appendices

6.1 Patterns of Sequences

6.2 Alternating Patterns of Sequences

6.3 Finite Series

6.4 Convergent Infinite Series

6.5 Periodicity and Modulo Arithmetic

6.5.1 Alternating Periodicity

6.6 Patterns as an Initial Value Problem

6.7 Specific Periodic Patterns

Bibliography

Index