Phyllotaxis and patterns on plants

Equations for coupled modelw(r, α, t)f (r, α, t)g(r, α, t)Surface normal deformationAiry Stress tensorGrowth/fluctuation auxin concentrationζw t + D∆ 2 w + N∆ χ w + 1R α∆ ρ f − [f , w] + κw + γw 3 = 01Eh ∆2 f − 1R α∆ ρ w + 1 2[w, w]+∆g = 0g t = −Lg − H ▽ 2 g − ▽ 4 g − ¯κ 1 ▽ (g ▽ g) − ¯κ 2 ▽ (▽g ▽ 2 g) −δg 3 + β∆fAlan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants