Abstract: The recurrence relation that represents the Fibonacci sequence is given by the second-order linear difference equation. Firstly, The parameter conditions of asymptotic stability of zero solution of generalized Fibonacci equation are discussed. Secondly, the dynamic properties of the above generalized Fibonacci equation under nonlinear perturbations are considered, the parametric conditions under which the nonlinear perturbations do not destroy the asymptotic properties of the zero solution of the linear approximate system are obtained through analysis, so that the asymptotic stability of the zero solution of the system can be determined by the asymptotic stability of the zero solution of the linear approximate system. The parameter conditions of asymptotic stability of zero solution under nonlinear disturbance are given.