## A study of the motions of two strongly coupled Van der Pol oscillators |

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### Contents

Coefficients of trigonometric functions from the righthand side | 8 |

Coefficients of trigonometric functions from the righthand side | 13 |

Stability of Equilibria | 21 |

7 other sections not shown

### Common terms and phrases

2ABD+C 2ACD+B ab(b amplitudes and periods analytical predictions analytical results approximate solutions bifurcation occurs coefficients correspond coso)^S Det(j differential equations eigenvectors equations 2.1 equations 2.27 equilibria are identical fast Fourier transform four equilibrium points Fourier given by Ccf Jacobian matrix l+2s large values limit cycle linear normal modes minor mode normal modes e=0 normal modes NRM's numerical and analytic numerical integration numerical results original co-ordinates x^,x2 original system oscillations occurs oscillators are exactly parameter values partial derivative phase difference phase-locked periodic motion phase-locked solutions Pol oscillators polar co-ordinates Q equilibria considered Q plane quasi-periodic motion radians range of values resonance right hand side Runge-Kutta method saddle unstable secular resonance secular terms sense of Rosenberg shown in fig side of equation sin(2x+y sinusoidal phase-locked motion Stability of Equilibria stable node system of equations tion total amplitude Tr(J transform to polar trigonometric functions Trigonometric Identities turbation U-Det(J U^+U yg obtained