Global behavior of nonlinear difference equations of higher order with applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Series: | Mathematics and its applications
256 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 228 S. |
| ISBN: | 079232286X |
Staff View
MARC
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| 245 | 1 | 0 | |a Global behavior of nonlinear difference equations of higher order with applications |c by V. L. Kocic and G. Ladas |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a XI, 228 S. | ||
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Record in the Search Index
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| adam_text | Contents
Preface ix
Acknowledgements xi
1 Introduction and Preliminaries 1
1.1 An Overview 1
1.2 Oscillation and General Background 4
1.3 Stability and General Background 8
1.4 Periodicity and General Background 15
1.5 Global Attractivity for First Order Equations 17
1.6 Some Basic Lemmas 19
1.7 Some Useful Theorems from Analysis 24
1.8 Notes 25
2 Global Stability Results 27
2.1 Global Asymptotic Stability of xn+i — xn/(xn,a;n_i) 27
2.2 Permanence of xn+i = xnf(xn,xn k1, ¦¦ ,xn kr) 35
2.3 Global Attractivity of xn+1 = xnf(xn,xn k1, ,xn kr) 39
2.4 Global Attractivity of xn+i = axn + F(xn k) 46
2.5 Global Stability of xn+1 = £*L0 a,xn_, + (1 A)F(YT=o 6^ ) ¦ • • 48
2.6 Notes 53
3 Rational Recursive Sequences 55
3.1 The Rational Recursive Sequence xn+i = (a + bxn)/(l + J3,=o aixn i) 56
3.2 The Rational Recursive Sequence
xn+l = (a+ E?=o «•¦*« .¦)/( +£?=ok*» .0 59
3.3 Global Stability of xn+1 = l/(£?=0 6,xn_.) 64
3.4 Global Stability of xn+1 = (a + bxn)/(A + xn.k) 67
3.5 Notes 74
vi Contents
4 Applications 75
4.1 A Discrete Delay Logistic Model 75
4.2 A Simple Genotype Selection Model 80
4.3 Periodicity in a Simple Genotype Selection Model 87
4.4 A Model of the Spread of an Epidemic 99
4.5 Nicholson s Blowflies 105
4.6 A Discrete Analogue of a Model of Haematopoiesis Ill
4.7 A Discrete Baleen Whale Model 119
4.8 A Semidiscretization of a Delay Logistic Model 123
4.9 A Discrete Analogue of the Emden Fowler Equation 125
4.10 Notes 132
5 Periodic Cycles 133
5.1 An Invariance for xn+1 = s^*, **2 135
5.2 The Five Cycle: xn+2 = i±^± 138
5.3 The Eight Cycle: xn+3 = 1+x»v+x * 141
5.4 Symmetric Periodic Sequences 144
5.5 Notes 152
6 Open Problems and Conjectures 153
6.1 The Rational Recursive Sequence xn+i = (a + bxn)/(A + xn i) .... 153
6.2 The Rational Recursive Sequence xn+ = {a f bx )/(c + i^J .... 155
6.3 A Model for an Annual Plant 159
6.4 The Dynamics of xn+1 = Ax~2 + x~l{2 162
6.5 A Discrete Model with Quadratic Nonlinearity 166
6.6 A Logistic Equation with Piecewise Constant Argument 168
6.7 Discrete Epidemic Models 169
6.8 Volterra Difference Equations 169
6.9 Global Attractivity of xn+1 — xn + pxn_k = f(xn m) 170
6.10 Neural Networks 172
6.11 The Fibonacci Sequence Modulo ir 174
6.12 Notes 176
Appendix 177
A The Riccati Difference Equation 177
B A Generalized Contraction Principle 189
Contents vii
C Global Behavior of Systems of Nonlinear Difference Equations 195
C.I A Discrete Epidemic Model 195
C.2 A Plant Herbivore System 197
C.3 Discrete Competitive Systems 199
Bibliography 205
Subject Index 223
Author Index 225
|
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| id | DE-604.BV008017647 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:12:57Z |
| institution | BVB |
| isbn | 079232286X |
| language | English |
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| physical | XI, 228 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Kocic, V. L. Verfasser aut Global behavior of nonlinear difference equations of higher order with applications by V. L. Kocic and G. Ladas Dordrecht u.a. Kluwer Acad. Publ. 1993 XI, 228 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 256 Équations aux différences non linéaires - Solutions numériques Nonlinear difference equations Numerical solutions Nichtlineare Differenzengleichung (DE-588)4501519-3 gnd rswk-swf Nichtlineare Differenzengleichung (DE-588)4501519-3 s DE-604 Ladas, Gerasimos E. Verfasser aut Mathematics and its applications 256 (DE-604)BV008163334 256 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005274850&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kocic, V. L. Ladas, Gerasimos E. Global behavior of nonlinear difference equations of higher order with applications Mathematics and its applications Équations aux différences non linéaires - Solutions numériques Nonlinear difference equations Numerical solutions Nichtlineare Differenzengleichung (DE-588)4501519-3 gnd |
| subject_GND | (DE-588)4501519-3 |
| title | Global behavior of nonlinear difference equations of higher order with applications |
| title_auth | Global behavior of nonlinear difference equations of higher order with applications |
| title_exact_search | Global behavior of nonlinear difference equations of higher order with applications |
| title_full | Global behavior of nonlinear difference equations of higher order with applications by V. L. Kocic and G. Ladas |
| title_fullStr | Global behavior of nonlinear difference equations of higher order with applications by V. L. Kocic and G. Ladas |
| title_full_unstemmed | Global behavior of nonlinear difference equations of higher order with applications by V. L. Kocic and G. Ladas |
| title_short | Global behavior of nonlinear difference equations of higher order with applications |
| title_sort | global behavior of nonlinear difference equations of higher order with applications |
| topic | Équations aux différences non linéaires - Solutions numériques Nonlinear difference equations Numerical solutions Nichtlineare Differenzengleichung (DE-588)4501519-3 gnd |
| topic_facet | Équations aux différences non linéaires - Solutions numériques Nonlinear difference equations Numerical solutions Nichtlineare Differenzengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005274850&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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