1. Consider the following model proposed many years ago by Gierer & Mein hardt: z = - y = -ay + Does increase of help (activate) or harm (inhibit) y? Does increase of y activate or inhibit x? This is called an activator-inhibitor syste, Whichs is the activator and which is the inhibitor? r, a are positive constants. Find the equilibrium. Write down the Jacobian matrix and evaluate it at the equilibria. Find the determinant and trace. Let a = 0.25. For what values of r is the equilibrium stable. For what value of r is the trace 0 and thus there is a Hopf bifurcation? Numerically solve the equations for a = 25, r = 0.3, 0.2, 0.1 with z(0) = 0.13, y(0) = 0.45. For which of these is the equilibrium stable? I have made Matlab and XPP (my 1. Consider the following model proposed many years ago by Gierer & Mein hardt: z = - y = -ay + Does increase of help (activate) or harm (inhibit) y? Does increase of y activate or inhibit x? This is called an activator-inhibitor syste, Whichs is the activator and which is the inhibitor? r, a are positive constants. Find the equilibrium. Write down the Jacobian matrix and evaluate it at the equilibria. Find the determinant and trace. Let a = 0.25. For what values of r is the equilibrium stable. For what value of r is the trace 0 and thus there is a Hopf bifurcation? Numerically solve the equations for a = 25, r = 0.3, 0.2, 0.1 with z(0) = 0.13, y(0) = 0.45. For which of these is the equilibrium stable? I have made Matlab and XPP (my