Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.
According to the results of electrochemical measurements and X-ray photoelectron spectroscopy, the degradation of the commercial alkaline cleaning solution originated from the oxidation of the commercial amino-group corrosion inhibitor in it, thus resulting in the formation of CuO film from native Cu2O film.
DOC inputs to soil solution originate from biological decomposition, throughfall or litter leaching, root exudates and from deposition of soot and dust (Wang et al. 2013).
The existence of a singularity during integration required "matching" of two solutions originating from the leading edge and the origin.
Precisely, one seeks for the existence of a family of T-periodic solutions originating from a limit cycle x 0 of the autonomous unperturbed system.
The existence of at least two branches of T-periodic solutions originating from x 0 is shown in [12, 13] and their stability, in the sense of Lyapunov, follows from the results of [14, 15].
The paper deals with the problem of the existence of a branch of T-periodic solutions originating from the isolated limit cycle of an autonomous parabolic equation in a Banach space when it is perturbed by a nonlinear T-periodic term of small amplitude.
This equation has a branch of solutions originating from x 0 ( θ 0 ) if the Malkin bifurcation function given by M = ∫ 0 T 〈 Q ˜ ( x 0 , 0 ) ( t ), z 0 ( t + θ ) 〉 d t, θ ∈ [ 0, T ], has θ 0 ∈ [ 0, T ] as simple zero.
During this period Gaudí perfected his personal style, inspired by the organic shapes of nature, putting into practise a whole series of new structural solutions originating from his deep analysis of ruled geometry.
