TY - JOUR

T1 - Chaos of the relativistic parametrically forced van der Pol oscillator

AU - Ashkenazy, Y.

AU - Goren, C.

AU - Horwitz, L. P.

PY - 1998/6/29

Y1 - 1998/6/29

N2 - A manifestly relativistically covariant form of the van der Pol oscillator in 1 + 1 dimensions is studied. We show that the driven relativistic equations, for which x and t are coupled, relax very quickly to a pair of identical decoupled equations, due to a rapid vanishing of the "angular momentum" (the boost in 1 + 1 dimensions). A similar effect occurs in the damped driven covariant Duffing oscillator previously treated. This effect is an example of entrainment, or synchronization (phase locking), of coupled chaotic systems. The Lyapunov exponents are calculated using the very efficient method of Habib and Ryne. We show a Poincaré map that demonstrates this effect and maintains remarkable stability in spite of the inevitable accumulation of computer error in the chaotic region. For our choice of parameters, the positive Lyapunov exponent is about 0.242 almost independently of the integration method.

AB - A manifestly relativistically covariant form of the van der Pol oscillator in 1 + 1 dimensions is studied. We show that the driven relativistic equations, for which x and t are coupled, relax very quickly to a pair of identical decoupled equations, due to a rapid vanishing of the "angular momentum" (the boost in 1 + 1 dimensions). A similar effect occurs in the damped driven covariant Duffing oscillator previously treated. This effect is an example of entrainment, or synchronization (phase locking), of coupled chaotic systems. The Lyapunov exponents are calculated using the very efficient method of Habib and Ryne. We show a Poincaré map that demonstrates this effect and maintains remarkable stability in spite of the inevitable accumulation of computer error in the chaotic region. For our choice of parameters, the positive Lyapunov exponent is about 0.242 almost independently of the integration method.

UR - http://www.scopus.com/inward/record.url?scp=0043286606&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(98)00240-0

DO - 10.1016/S0375-9601(98)00240-0

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AN - SCOPUS:0043286606

SN - 0375-9601

VL - 243

SP - 195

EP - 204

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 4

ER -