Abstract
An analytical threshold condition for the prediction of horseshoe chaos is obtained for the Bonhoeffer-van der Pol (BVP) oscillator, through the equivalent Duffing-van der Pol (DVP) oscillator, using the Melnikov method. Numerical and analytical predictions of the tangential intersection of stable and unstable orbits of saddle have been compared for both the DVP and BVP oscillators. The analytical threshold of the BVP oscillator, derived by extrapolating that of the DVP oscillator, is found to be in good agreement with the actual numerical analysis of the system.
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