Exact homoclinic and heteroclinic solutions of the Gray-Scott model for autocatalysis

SIAM Journal on Applied Mathematics

Volumn 61, Issue 1, 2000, Pages 102-130

  Hale, J K ^a   Peletier, L A ^a   Troy, W C ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Gray Scott model; Heteroclinic orbits; Homoclinic orbits; Reaction diffusion

Indexed keywords

APPROXIMATION THEORY; CATALYSIS; DIFFUSION; FUNCTION EVALUATION; INITIAL VALUE PROBLEMS; INTEGRAL EQUATIONS; THEOREM PROVING;

AUTOCATALYSIS; GRAY-SCOTT MODEL; HETEROCLINIC ORBITS; HOMOCLINIC ORBITS;

MATHEMATICAL MODELS;

EID: 0034458192     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139998334913     Document Type: Article

References (34)

1. The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves
2. The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. II. An initial-value problem with an immobilized or nearly immobilized autocatalyst
3. The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. III. Large time development in quadratic autocatalysis
4. An example of bifurcation to homoclinic orbits
5. Blue sky catastrophes in reversible and Hamiltonian systems
6. AUTO97: Continuation and bifurcation software for ordinary differential equations
7. Numerical evidence of sationary and breathing concentration patterns in the Oregonator with equal diffusivities
8. Pattern formation in the one-dimensional Gray-Scott model
9. Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system
10. Autocatalytic reactions in the isothermal continuous stirred tank reactor: Isolas and other forms of multistability
11. Autocatalytic reactions in the isothermal continuous stirred tank reactor: Oscillations and instabilities in the system A + 2B → 3B, B → C,
12. Sustained oscillations and other exotic patterns of behavior in isothermal reactions
13. Nonlinear oscillations, dynamical systems and bifurcation of vector fields
14. Introduction to dynamic bifurcation
15. Stability and instability in the Gray-Scott model: The case of equal diffusivities
16. Using Mel'nikov's method to solve Sil'nikov's problems
17. On the stability of the center for time periodic perturbations
18. Exponential dichotomies and transversal homoclinic points
19. Dynamics of self-replicating patterns in reaction diffusion systems
20. A bifurcation sequence to stationary spatial patterns in a nonuniform chemical model system with equal diffusion coefficients
21. Homoclinic period blowup in reversible and conservative systems
22. Chemical pattern formation with equal diffusion coefficients
23. Turing patterns in an open reactor
24. Global bifurcation and chaos: Analytical methods