def test_singular_equilibrium(self): N, L, Delta, theta, gamma = self.positive_toggle() pos_cfs = CyclicFeedbackSystem(N, L, Delta, theta, gamma) x = pos_cfs.singular_equilibrium() assert (np.allclose(x(.1), np.array([[1.5], [1.5]]))) N, L, Delta, theta, gamma = self.neg_edge_toggle() pos_cfs = CyclicFeedbackSystem(N, L, Delta, theta, gamma) U1 = Delta[0, 1] + L[0, 1] U2 = Delta[1, 0] + L[1, 0] theta1 = theta[0, 1] theta2 = theta[1, 0] Delta1 = Delta[0, 1] Delta2 = Delta[1, 0] s = sympy.symbols('r') eps_func = sympy.Matrix([[0, 1], [1, 0]]) * s s_val = .1 eps1 = s_val eps2 = s_val m1 = Delta1 / (2 * eps1) m2 = Delta2 / (2 * eps2) #solution for gamma1 = gamma2 = 1 x1 = (U1 + (theta1 - eps1 - U2) * m1 - (theta2 - eps2) * m1 * m2) / (1 - m1 * m2) x2 = (U2 + (theta2 - eps2 - U1) * m2 - (theta1 - eps1) * m1 * m2) / (1 - m1 * m2) expected = np.array([[x1], [x2]]) x = pos_cfs.singular_equilibrium(eps_func) assert (np.allclose(x(s_val), expected))
def test_pos_bifurcations(self): N, L, Delta, theta, gamma = self.neg_edge_toggle() cfs = CyclicFeedbackSystem(N, L, Delta, theta, gamma) s = sympy.symbols('s') eps_func = sympy.Matrix([[0, 1], [1, 0]]) * s x_eq = cfs.singular_equilibrium(eps_func, lambdify=False) zero_crossings = cfs.j_border_crossings(0, x_eq, eps_func) assert (len(zero_crossings) == 1) for crossing in zero_crossings: assert (np.allclose(crossing[0], .3162, rtol=1e-4)) assert (np.allclose(cfs(crossing[1], np.array([[0, .3162], [.3162, 0]])), np.zeros([2, 1]), atol=1e-4)) crossings, eps_func_out = cfs.border_crossings(eps_func) assert (eps_func_out == eps_func) assert (crossings[0][0][0] == zero_crossings[0][0]) assert (len(crossings[1]) == 1) for crossing in crossings[1]: assert (np.allclose(crossing[0], .67202)) assert (np.allclose(cfs(crossing[1], np.array([[0, .67202], [.67202, 0]])), np.zeros([2, 1]), atol=1e-4)) #get_bifurcations bifurcations = cfs.get_bifurcations(eps_func)[0] assert (not cfs.in_singular_domain( x_eq.subs(s, .37202), np.array([[0, .37202], [.37202, 0]]), 1)) assert (len(bifurcations[0]) == 1) for s_val in bifurcations[0]: assert (np.allclose(s_val[0], .3162, rtol=1e-4)) #make sure border_crossings runs on three nodes cfs = CyclicFeedbackSystem(*self.three_node_network()) crossings, eps_func = cfs.border_crossings() assert (True)