A new type of intermittency from a ring of four coupled phase-locked loops

Hasegawa, Akio; Komuro, M.; Endo, Tetsuro; Igarashi, R.

doi:10.1109/81.678474

Cited by 16 publications

(17 citation statements)

References 11 publications

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“…The dynamics within each of the three-dimensional subspaces can be chaotic, and attractors may include points within (or be 'stuck on' to) these subspaces and hence typical trajectories show intermittency where they remain for arbitrarily long times in arbitrarily small neighbourhoods of the invariant subspace. This leads to the appearance of on-off and other types of intermittency; see for example [ll, 13,19,20,261; for reviews, see for example [5, 241. This leads on to the second aim of the paper; to investigate in detail some examples of intermittent dynamics of some attractors for the model (4) where the dynamics is intermittent to more than one invariant subspace. Although intermittent dynamics has been found previously in examples of mean field dynamos, as far as we are aware this is the first example of twestate intermittency in such a model that involves chaotic saddles within the invariant subspaces.…”

Section: Introductionmentioning

confidence: 99%

Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

Ashwin

Rucklidge

Sturman

2004

Physica D: Nonlinear Phenomena

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Article:Ashwin, P., Rucklidge, A.M. and Sturman, R. (2004) Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory. Physica D: Nonlinear Phenomena, We consider a irlodel of a Hopf bif~rcat~iorl intera~t~ing as a codiirlerlsiorl 2 bifurcation ~it~l.1 a saddle-node on a liirlit cycle, irl~t~ivat~ed by a low-order irlodel for magnet,ic act,ivit,y in a stellar dynamo. This irlodel corlsist,~ of coupled irlt,eract,iorls between a saddlenode arld t,wo Hopf bifurcat>ions, where the saddlenode bif~rcat~iorl is assuirled t,o liave global reirljectiorl of t,raject,ories. The irlodel car1 produce cl.laot,ic beliaviour wit,liin each of a pair of invariant subspaces, and also it can show at,t,ract,ors t>klat are stuck-on to b0t~l.1 of t,he inrrariant, subspaces. We imest,igat,e t,he det>ailed intjerinitjtjentj dyrlairlics for such an at,t,ract,or, irlriest,igat,irlg t,he effect of breaking t,he ~yirlirlet~ry bet>weerl t,he t,wo Hopf bifurcations, and observing t,l.lat it can appear via blowout, bif~rcat~iorls froirl t,he invariant subspaces.We give a siirlple llarkov chain irlodel for t,he t,west,at,e irlt,erinit,t,ent dyrlairlics t,l.iat, reproduces t,he t,iirle spent close t,o t,he invariant subspaces and t,he swit,cl.ling bet,weerl t,he different, possible i11variant~ subspaces: t>klis clarifies t,he obser~rat~ion t>klat t,he prop~rt~iorl of t>iirle spent, near the different subspaces depends on the average residence t>iirle and also on the pr~babilit~ies of ~wit~ching bet>weerl t,he possible subspaces. *P.Asl

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Section: Introductionmentioning

confidence: 99%

Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

Ashwin

Rucklidge

Sturman

2004

Physica D: Nonlinear Phenomena

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“…In the following, the entrance set and the exit set are derived by computer simulation in a manner similar to that in Ref. 6. Figure 11(a) shows the results.…”

Section: Generating Mechanism Of Onoff Intermittencymentioning

confidence: 98%

“…6, there are numerous saddletype equilibrium points outside H. The numerous stable manifolds spanned by these points become a separatrix scattering out the orbits started from the initial values in various directions. These orbits then are attracted to the entrance set of H again from totally different directions.…”

Section: Behavior Of the Orbit Outsidementioning

confidence: 99%

“…1(b) on the output phase T i can be obtained by letting the VCO output voltage of the i-th PLL be U i C C2 AcosZ 0 t T i t [Z 0 : free running angular frequency, T i t: output phase]. From this, the following equation can be derived [6]:…”

Section: Modelingmentioning

confidence: 99%

“…By changing the coupling factor V, this system exhibits various types of chaos typified in a high-dimensional system, and is especially interesting in that several new types of intermittency including onoff intermittency are exhibited in a real system [6]. The present paper focuses our attention on onoff intermittency.…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

On-off intermittency from a ring of four-coupled PLLs

Hasegawa

Endo

Komuro

2000

Electron. Comm. Jpn. Pt. II

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Bifurcations and intermittent chaos observed in a ring of four‐coupled PLLs

Hasegawa

Komura

Endo

et al. 2002

Electron Comm Jpn Pt III

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SUMMARYIn this paper, we study various types of bifurcations of attractors observed in computer simulation and electronic circuit experiment of the ring of four-coupled PLLs when coupling coefficient σ is increased and the route to chaos is made clear. In particular, for intermittent chaos that is observed when σ becomes large, we study the laminar distribution, time variation of local expansion rate, and Lyapunov exponent. We have shown the existence of several kinds of intermittent chaos with different properties.

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A new type of intermittency from a ring of four coupled phase-locked loops

Cited by 16 publications

References 11 publications

Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

On-off intermittency from a ring of four-coupled PLLs

Bifurcations and intermittent chaos observed in a ring of four‐coupled PLLs

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