Nussbaum R.D., Peitgen H. Special and spurious solutions of x(t)=-a f(x(t-1))

Providence: American Mathematical Society, 1984. — 141 p.Phase Plane Studies of a Cyclic SystemSymmetries in the phase plane and their involutions
Three typical time-continuous studies
Special C and PL models and numerical experiments
Existence of hetero- and homoclinic points
Homoclinic bifurcation and phase transitionsContinua of Special Periodic SolutionsReduction to a cyclic system of ODE's and a fixed point problem
Linear theory
Nodal theory
A priori estimates for special periodic solutions
Bifurcation from infinity
Other nonlinearitiesNumerical Approximation and Spurious SolutionsDerivation of the approximation scheme
Existence of spurious solutions
ExperimentsA Prioribounds without the Assumption of OddnessA priori estimates for slowly oscillating periodic solutions
Existence of slowly oscillating periodic solutions