Difference equations and discrete dynamical systems with applications: 24th ICDEA, Dresden, Germany, May 21-25 2018

Scientific Committee......Page 6
Preface to Proceedings of ICDEA 2018......Page 7
Contents......Page 9
Papers by Plenary Speakers......Page 11
 1 Introduction......Page 12
 2 Auxiliary Results......Page 17
 3 Main Results......Page 20
 4 Applications......Page 21
  4.1 Pielou\'s Equation with Several Arguments......Page 22
  4.2 Generalized Ricker Model with Variable Arguments......Page 24
  4.3 Lasota–Wazewska Equation......Page 25
 5 Final Comments......Page 27
 References......Page 28
 1 Introduction......Page 29
  2.1 The Critical Set......Page 34
  2.2 Stable and Unstable Sets......Page 35
  3.1 The Mandelbrot Set calM1 of the Quadratic Map......Page 36
  3.2 The Mandelbrot Set calMλ for Decreasing λ......Page 38
  3.3 Rescaling and Bifurcation Set for cinmathbbR......Page 41
  4.1 Julia Sets for Fixed c inmathbbR......Page 43
  4.2 From the Period-One to the Period-Two Region of calM0.98......Page 47
 5 Conclusions......Page 57
 References......Page 61
 1 Introduction......Page 63
 2 Background: Tools and Techniques......Page 70
  2.1 Linear Theory......Page 71
  2.2 Existence of Waves......Page 75
  2.3 Stability of Waves......Page 81
  2.4 Numerical Aspects......Page 85
 3 Periodic Patterns......Page 86
  3.1 Multichromatic Waves......Page 87
  3.2 Negative Diffusion......Page 90
  3.3 Competing Interactions......Page 91
 4 Nagumo Equations on Planar Lattices......Page 92
  4.1 Linear Theory......Page 94
  4.2 Local Stability......Page 97
  4.3 Global Stability......Page 99
  4.4 Spreading Phenomena......Page 101
  4.5 Travelling Corners......Page 102
  4.7 Travelling Checkerboards......Page 104
 5 Discrete FitzHugh–Nagumo Equations......Page 105
  5.1 Singular Perturbation Theory......Page 106
  5.2 Periodic Diffusion......Page 108
  5.3 Infinite-Range Interactions......Page 109
  6.1 Spatial-Temporal Discretizations......Page 110
  6.2 Adaptive Grids......Page 112
 References......Page 114
Contributed Papers......Page 121
  1.1 Notation......Page 122
  1.2 Fractional Difference Operators......Page 124
 2 Exponentially Weighted ellp Spaces......Page 125
 3 mathcalZ Transform......Page 127
 4 Fractional Difference Equations on ell2, ρ(mathbbZ; H)......Page 131
 References......Page 137
 Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems......Page 139
 2 Problem Statement......Page 140
 3 Comparisons and Discussions of Assignability Problems......Page 145
 4 Conclusions and Open Problems......Page 152
 References......Page 153
 1 Introduction......Page 154
 2 Exponential Separation in Bounded and Unbounded Systems: General Properties......Page 156
 3 Strongly Exponentially Separated Systems......Page 160
 5 Roughness of Strong Exponential Separation......Page 168
 6 Exponential Separation in Block Upper Triangular Systems......Page 179
 7 Exponential Separation in Linear Symplectic Systems......Page 187
 References......Page 190
 1 Introduction......Page 192
 2 Time Scales......Page 194
 3 Dynamic SIS Model......Page 196
 4 Dynamic SIS Model with Vital Dynamics......Page 201
 References......Page 204
 1 Nonlinear Leslie Matrix Equations......Page 206
 2 Equilibria......Page 209
 3 Equilibrium Stability......Page 210
 4 An Application......Page 212
 References......Page 215
 1 Introduction......Page 217
 2 Peak Effect for Second-Order Difference Equations......Page 219
  3.1 The Heavy Ball Method......Page 221
  3.2 Convergence Analysis......Page 223
  3.3 Peak Effect......Page 225
  4.1 Construction of the Lyapunov Function......Page 226
  4.2 Global Convergence......Page 231
  4.3 Adaptive Algorithm......Page 232
 5 Conclusion......Page 233
 References......Page 234
 1 Introduction......Page 235
 2 Statement of the Problem......Page 236
  3.1 DEPCA: Reduction to Discrete Maps......Page 237
  3.2 Related Interval Maps......Page 239
 4 Main Results......Page 240
  4.1 Squeezing Sequences of Imbedded Intervals......Page 241
  4.2 Global Attractivity Under Unimodal Families......Page 242
  4.3 Critical Case λ=0......Page 248
  4.4 Examples......Page 250
 5 Discussion......Page 253
 References......Page 254
 1 Introduction......Page 255
 3 Auxiliary Results......Page 258
 4 Proofs of Main Results......Page 261
 5 An Example......Page 265
 6 Final Discussion......Page 266
 References......Page 268
 1 Introduction......Page 270
 2 General Results......Page 272
  3.1 When g Is a Rational Function with Similar Numerator and Denominator......Page 280
  3.2 Establishing Boundedness Character (B,U)......Page 286
  4.1 Finding an Unbounded Solution Using Three Iterations......Page 288
  4.2 A Solution with Nonperiodic Coefficients......Page 292
 5 Conclusion......Page 296
 A  Boundedness Character of System (2)......Page 297
 References......Page 298
 Stability Investigation of Biosensor Model Based on Finite Lattice Difference Equations......Page 299
 1 Introduction......Page 300
 2 Deriving the Difference Equations Model......Page 301
 3 Permanence......Page 303
  4.1 Steady States......Page 309
  4.2 Global Attractivity......Page 310
 5 Numerical Investigation......Page 314
 6 Conclusions......Page 321
 References......Page 322
 1 Motivation......Page 324
  2.1 Reaction......Page 326
  2.2 Dispersion......Page 327
  2.4 Homogeneous Boundary Conditions......Page 328
 3 Equilibria and Their Stability......Page 329
  3.1 Particular Case......Page 331
 References......Page 333
 1 Introduction......Page 335
 2 Oscillation of Half-Linear Dynamic Equations......Page 337
 3 Oscillation of Nonlinear Dynamic Equations......Page 341
 4 Oscillation Constants for Euler Type Linear Dynamic Equations and Their Perturbations......Page 342
 5 Asymptotic Formulae......Page 347
 References......Page 352
 1 Introduction......Page 354
 2 Stability and Instability Regions......Page 355
 3 Final Remarks......Page 362
 References......Page 363