Busse balloons - from the reversible Gray-Scott model ... - Eurandom

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$Continuous-time random walks, fractional calculus and ... - Eurandom$

Busse balloon Introduction Rise of Patterns The Busse balloon Conclusions and ongoing research ◮ The Eckhaus band is only the beginning! The complete region of stable patterns in (A, k)-space is called the Busse balloon. ◮ No mathematical analysis possible! → but numerics! Continuation and bifurcation software (Auto) Sjors van der Stelt Busse balloons
Introduction Rise of Patterns The Busse balloon Conclusions and ongoing research Example: Busse balloon for Gray-Scott system k 17.5 15.0 12.5 10.0 7.5 5.0 2.5 sn 1 Hopf +1 sideband 0.0 0.000 0.010 0.020 0.030 0.040 0.050 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 sn 2 equilibrium A Busse balloon sideband 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 equilibrium sideband sn 1 Hopf+1 Hopf−1 Figure: A Busse balloon for the Gray-Scott model with b = ... and γ = 1. Sjors van der Stelt Busse balloons
Page 1 and 2: Introduction Rise of Patterns The B
Page 3 and 4: The Model Introduction Rise of Patt
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Page 7 and 8: Birth of patterns Introduction Rise
Page 13: Busse balloon Introduction Rise of
Page 21 and 22: Conclusions Introduction Rise of Pa
Page 23 and 24: Conclusions Introduction Rise of Pa
Page 25 and 26: Ongoing research Introduction Rise

Busse balloons - from the reversible Gray-Scott model ... - Eurandom

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