l16_notes

l16_notes - Review L15 Turing-Gierer-Meinhardt models Local...

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Unformatted text preview: Review L15 Turing-Gierer-Meinhardt models Local excitation, global inhibition 2 2 2 2 2 2 x i D i a k t i x a D a i a k r t a i i i a a a a + = + + = a: concentration activator i: concentration inhibitor t: time x: position variables r a : basal activator synthesis rate k a , k i : rate constant for synthesis a , i : decay rates D a , D i : diffusion constants constants (parameters) 1 2 2 2 2 2 2 x i D i a k t i x a D a i a k r t a i i i a a a a + = + + = choose dimensionless variable normalize 4 variables ( ) 2 2 2 2 2 2 1 s I P I A Q I s A A I A R A + = + + = 2 ) 1 ( 1 + = + = R I R A homogeneous solution / / = = t s 2 homogeneous solution / / = = t s A 3 A s I I s stability of homogeneous solution + + + = Q Q R R R R R Q Q A...
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l16_notes - Review L15 Turing-Gierer-Meinhardt models Local...

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