Time-periodic solutions of the partial differential equation set for a one-dimensional model of a radio-frequency plasma are computed directly by finite-difference discretization of the equations and by Newton's method for computing the time-periodic states of periodically forced ordinary differential equations.
The grazing bifurcation, stick phenomena and periodic motions in a periodically forced, nonlinear friction oscillator are investigated.
By Gaines-Mawhin's continuation theorem, Jódar et al. [17] obtained that a T-periodic solution exists for a more general system whenever the condition (min_{tinmathbb{R}} beta(t)> gamma+ mu) holds; Bai and Zhou [18], Bai et al. [19], and Liu [20] studied the existence of periodic solutions for a periodically forced SIR model with saturated incidence rates.
When (f(I equiv1) in (1.1), Katriel [16] got the existence of periodic positive solutions for the periodically forced SIR model by Leray-Schauder degree theory provided (mathcal{R}_{0}>1).
Simulations of a periodically forced CSTR reveal several jumps in forced system qualitative behavior as the forcing frequency is altered.
Nonlinear chemical process systems which are periodically forced do not necessarily have unique, stable periodic responses with the same period as the input, although such behavior has been widely assumed previously.
Lin et al. [200] demonstrate that the ML model can exhibit shear-induced chaos near the homoclinic bifurcation when periodically forced, by plotting images of the periodic orbit under successive applications of the kick map and calculating the maximum Lyapunov exponent.
We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions.
The approach presented is motivated by the observation, that stirred tank reactors operated in batch, semi-batch, continuous, or even periodically forced mode can be subsumed by a single optimization model with periodicity constraints and suitably chosen model equations and decision variables.
Periodically force-fed in a hospital, she is protesting the laws shielding security forces from prosecution in an insurgency-racked corner of the northeast.
