Open AccessTwo-Dimensional Manifolds of Modified Chen System with Time Delay
Author(s) -
Suqi Ma
Publication year - 2021
Publication title -
international journal of bifurcation and chaos in applied sciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.761
H-Index - 103
eISSN - 1793-6551
pISSN - 0218-1274
DOI - 10.1142/s0218127421501741
Subject(s) - limit cycle , attractor , mathematics , center manifold , manifold (fluid mechanics) , limit (mathematics) , mathematical analysis , eigenvalues and eigenvectors , stable manifold , slow manifold , invariant manifold , instability , chen , physics , bifurcation , hopf bifurcation , nonlinear system , mechanics , geology , mechanical engineering , singular perturbation , paleontology , quantum mechanics , engineering
Two-dimensional unstable manifolds of the modified Chen system are constructed at equilibrium solution by “expanding up” along the unstable eigen-direction, hence it is tangent to the unstable eigenspace. In general, unstable manifold expands to the attraction basin of the corresponding limit cycle or attractor. With the introduction of time delay, the two-dimensional unstable manifold of an unstable focus is simulated via expanding solution orbits with restriction condition on the associated foliations. The simulated unstable manifold coincides with the attraction basin of the limit cycle of the delay differential equations.