Theory and Applications of Difference Equations and Discrete Dynamical Systems: ICDEA, Muscat, Oman, May 26 - 30, 2013 (Springer Proceedings in Mathematics & Statistics Book 102)

This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications. Preface 6 Conference Organizing and ScientificCommittees 8 Contents 9 Speakers at ICDEA 2013 11 Part IPapers by Invited Speakers 17 1 Competitive Exclusion Through Discrete Time Models 18 1 Introduction 18 2 Unstructured Models 20 3 Structured Models 26 4 Extending the Competitive Exclusion Result in [5] 33 References 35 2 Benford Solutions of Linear Difference Equations 37 1 Introduction 37 2 Basic Definitions and Tools 40 3 A Simple Special Case: Positive Matrices 44 4 The Case of Arbitrary Matrices 53 5 An Application to Markov Chains 66 References 72 3 Harvesting and Dynamics in Some One-Dimensional Population Models 75 1 Introduction 75 2 The Ricker Model and the Hydra Effect 76 2.1 Census Timing and the Hydra Effect 77 2.2 Variable Harvest Timing and Its Impact on Population Dynamics 79 3 The Ricker--Clark Model and the Bubbling Effect 80 4 The Ricker--Schreiber Model: Sudden Collapses and Essential Extinction 83 5 Conclusions 86 References 87 4 Chaos and Wild Chaos in Lorenz-Type Systems 88 1 Introduction 88 2 Chaos in the Lorenz System 92 2.1 Global Organisation of the Phase Space 93 2.2 From Lorenz Attractor to Lorenz Map 96 3 Wild Chaos in a Lorenz-Type System of Dimension Five 100 3.1 The Transition for Increasing a = λ 102 3.2 The Bifurcation Diagram in the (a, λ)-plane 107 4 Conclusions 108 References 109 Part IIContributed Papers 112 5 Almost Automorphic Sequences and Their Application to a Model of a Cellular Neural Network 113 1 Introduction 113 2 Preliminaries and Main Results 115 References 123 6 Advances in Periodic Difference Equations with Open Problems 124 1 Introduction 124 2 Periodic Orbits in Periodic Non-autonomous Systems 126 3 Folding in Periodic Systems 128 4 Merging Periodic Sequences 129 5 Commuting Maps and the Problem of Sharing Periodic Orbits 130 6 The Parrondo's Paradox 132 7 Applications 134 References 135 7 An Evolutionary Beverton-Holt Model 138 1 Introduction 138 2 Asymptotic Dynamics of the Evolutionary Beverton-Holt Model 141 3 Examples 146 4 Concluding Remarks 149 References 152 8 The Periodic Decomposition Problem 153 1 Introduction 154 2 Continuous Periodic Decompositions 156 3 Generalizations to Linear Operators 159 4 Application of the Operator Theoretic Results 165 4.1 The decomposition property of BC(mathbbR) 165 4.2 Applications to Lp spaces 167 4.3 More Spaces with the Decomposition Property 169 5 Results for Arbitrary Transformations 170 5.1 Unrelated Transformations 172 5.2 Invertible Transformations 173 6 Decompositions on Groups 174 7 Actions of Semigroups 175 8 Further Results 176 References 178 9 Existence of Periodic and Almost Periodic Solutions of Discrete Ricker Delay Models 180 1 Introduction 180 2 Preliminary Lemma 182 3 Periodic Models with Finite Delay 183 4 Almost Periodic Models with Finite Delay 185 5 Examples 189 6 Almost Periodic Models with Infinite Delay 191 References 194 10 Generalized Lagrange Identity for Discrete Symplectic Systems and Applications in Weyl--Titchmarsh Theory 195 1 Introduction 195 2 Lagrange Identity 197 3 Special Examples 200 4 Weyl--Titchmarsh Theory 203 References 210 11 Dynamic Selection Systems and Replicator Equations 211 1 Introduction 211 2 The Equations and Their Interpretation 212 3 Equivalence of Selection and Replicator Systems 216 References 221 12 Asymptotic Equivalence of Difference Equations in Banach Space 222 1 Introduction 222 2 Conjugacy of Difference Equations 225 3 Asymptotic Equivalence of Difference Equations 227 References 228 Front Matter....Pages i-xvi Front Matter....Pages 1-1 Competitive Exclusion Through Discrete Time Models....Pages 3-21 Benford Solutions of Linear Difference Equations....Pages 23-60 Harvesting and Dynamics in Some One-Dimensional Population Models....Pages 61-73 Chaos and Wild Chaos in Lorenz-Type Systems....Pages 75-98 Front Matter....Pages 99-99 Almost Automorphic Sequences and Their Application to a Model of a Cellular Neural Network....Pages 101-111 Advances in Periodic Difference Equations with Open Problems....Pages 113-126 An Evolutionary Beverton-Holt Model....Pages 127-141 The Periodic Decomposition Problem....Pages 143-169 Existence of Periodic and Almost Periodic Solutions of Discrete Ricker Delay Models....Pages 171-185 Generalized Lagrange Identity for Discrete Symplectic Systems and Applications in Weyl–Titchmarsh Theory....Pages 187-202 Dynamic Selection Systems and Replicator Equations....Pages 203-213 Asymptotic Equivalence of Difference Equations in Banach Space....Pages 215-222