Nagata, Yuta Meiji University
Inaba, Naohiko Meiji University
Sekikawa, Munehisa Utsunomiya University
Endo, Tetsuro Meiji University
Canards are interesting nonlinear phenomena that have generated intense research interest since their discovery in the late 20th century. We are interested here in how canard-generating dynamics are influenced by extremely weak periodic perturbations that cause the formation of saddle-node bifurcations in the fundamental harmonic entrainment region. In a previous study, we discovered that another entrainment region exists within the fundamental harmonic entrainment region surrounded by the second saddle-node bifurcation curves. We found that two pairs of stable and saddle canards coexist in this second entrainment region under such weak periodic perturbation. Moreover, the stable and saddle canards are matched pairwise; i.e., each stable canard quite closely resembles a corresponding saddle canard. Calculation of the correlation coefficients of the four canards revealed two similar solutions on the order of 0.9999⋯ between the two pairs of similar canards. In contrast, the correlation coefficients of the dissimilar canards differ from unity in proportion to the difference between the given bifurcation parameter value and the parameter values at the saddle-node bifurcation points. Approximately, they take values from 0.998 to 0.975. These contrasts are noteworthy. Similar bifurcation phenomena were observed in the 1/2-subharmonic entrainment region. We hypothesize that the two pairs of stable and saddle canards are invariant with respect to a slight shift of time at the saddle-node bifurcation points, and we numerically prove that such a property approximately holds at the bifurcation points.
Progress of Theoretical and Experimental Physics
The Physical Society of Japan|Oxford University Press
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