DBSolve Optimum includes a general continuation procedure, based on a tangent predictor continuation scheme [ 10].
By using a continuation theorem based on coincidence degree theory, they obtained sufficient criteria for the existence of periodic solutions for the system.
By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system.
In this paper, with the help of a continuation theorem based on Gaines and Mawhin's coincidence degree theory, we study the existence and multiplicity of periodic solutions of a ratio-dependent food chain model with exploited term(s).
By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate.
The continuation scheme, based on the QR decomposition, facilities parametric studies for design by using the system solution for one set of parameters to optimally predict the steady state periodic solution for a similar set of parameters.
To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response.
This paper presents a continuation algorithm based on the Asymptotic Numerical Method (ANM) to study instability phenomena of large torsion of thin-walled open sections beams under various external loadings.
For example, many authors have obtained the existence and multiplicity of periodic solutions by various methods, such as a generalized form of the Poincaré-Birkhoff theorem, critical point theory, phase-plane analysis combined with shooting methods or fixed point theorems of planar homeomorphisms, and continuation methods based on degree theory; see [1 7] and the references therein.
Some new sufficient conditions for ascertaining the existence and global exponential stability of the periodic solution of such BAM neural networks are obtained by using the properties of nonsingular M-matrix, integral inequality analysis and a continuation theorem based on coincidence degree.
