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Kundan Lal DAS Munehisa SEKIKAWA Tadashi TSUBONE Naohiko INABA Hideaki OKAZAKI
This paper discusses the synchronization of two identical canard-generating oscillators. First, we investigate a canard explosion generated in a system containing a Bonhoeffer-van der Pol (BVP) oscillator using the actual parameter values obtained experimentally. We find that it is possible to numerically observe a canard explosion using this dynamic oscillator. Second, we analyze the complete and in-phase synchronizations of identical canard-generating coupled oscillators via experimental and numerical methods. However, we experimentally determine that a small decrease in the coupling strength of the system induces the collapse of the complete synchronization and the occurrence of a complex synchronization; this finding could not be explained considering four-dimensional autonomous coupled BVP oscillators in our numerical work. To numerically investigate the experimental results, we construct a model containing coupled BVP oscillators that are subjected to two weak periodic perturbations having the same frequency. Further, we find that this model can efficiently numerically reproduce experimentally observed synchronization.
Hideaki OKAZAKI Katsuhide FUJITA Hirohiko HONDA Hideo NAKANO
This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.
Behavior of solutions related to an accuracy exp(-1/ε) is studied. Computer results are given, and examined from the view-point of non-standard analysis. The experimental results raise some important questions on the computer study of slow-fast systems.