Nonlinear chemical dynamics and pattern formation

Lingfa Yang

Contents

  1. Introduction
  2. Reaction-diffusion systems
    1. Patterns in chemical reactions
      1. Spirals waves in BZ reaction
      2. Turing patterns in CIMA reaction
    2. Mathematical biology
      1. The Algorithmic Beauty of Sea Shells
      2. Embryo pattern formation
      3. Mammalian coat patterns
    3. Pattern formation in semiconductors
    4. Patterns in gas-discharge systems
    5. Pattern formation in nanoclustering
    6. Neuron-glial network, Calcium waves and patterns
    7. Intelligent biomaterial
    8. Enzymatic oscillations
    9. Others
  3. Waves and Patterns
    1. Spiral waves
      1. Samples of spirals
      2. Normal spirals
      3. Antispirals, nucleation
      4. Segmented spirals
      5. Twisted spirals
    2. Target patterns
      1. Leading center/pacemaker
    3. Standing waves Chemical wave packet
    4. Turing patterns
      1. Classic Turing patterns
      2. Oscillatory Turing patterns
      3. Superlattice Turing patterns
      4. Spatial resonance
      5. Turing patterns in square lattices
      6. Frontier Turing in a 2-layer system
      7. Turing and waves
    5. Pattern formation with global feedback coupling
  1. Linear stability analysis and bifurcations
    1. Supercritical bifurcations
      1. Hopf bifurcation
      2. Turing bifurcation
      3. Codimension-2 Turing-Hopf
      4. Wave bifurcation
    2. Subcritical bifurcations
      1. Subcritical Hopf
      2. Subcritical Turing
      3. Subcritical wave
    3. Stability of limit-cycles (Floquet theory)
    4. Transverse instabilities of wavefronts
    5. Multiple stabilities
  2. Weak nonlinear analysis and pattern selection
    1. Multiple scaling analysis
      1. The cubic equation
      2. The quintic equation
    2. Square lattices
    3. Hexagonal lattices
  3. Secondary instabilities
    1. Newell-Whitehead-Segel equation
    2. Eckhaus instability
    3. Zig-zag instability
  4. Localized structures
    1. Localized Turing patterns
    2. Solitary waves
      1. Solitons
      2. Oscillons
      3. Jumping oscillons
  5. Appendix
    1. Typical reaction-diffusion models
      1. Brusselator
      2. Oregonator
      3. Realistic BZ model
      4. Lengyel-Epstein model (LE)
      5. FitzHugh-Nagumo model (FHN)
      6. Schnackenberg model
      7. Boissonade model
    2. Amplitude equations
      1. Hexagonal lattices
      2. Square lattices
      3. CGLE for Hopf
      4. The forced CGLE
      5. The quintic CGLE
      6. Codimension-2 issues
      7. Subharmonic problems
  6. Glossary
  7. Acknowledgments
  8. References