[PDF]    http://dx.doi.org/10.3952/lithjphys.50210

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 50, 167–173 (2010)


ANTICIPATING OF CHAOTIC STATES VIA ANTI-PHASE DIAGONAL COUPLING
T. Pyragienė and K. Pyragas
Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goštauto 11, LT-01108 Vilnius, Lithuania
E-mail: pyragiene@pfi.lt

Received 17 March 2010; accepted 17 June 2010

Anticipating synchronization is considered as a tool for a real-time forecasting of chaotic dynamics. An anti-phase diagonal coupling scheme is introduced in order to supply the long-term prediction of behaviour of a drive system. The efficiency of such a scheme is studied analytically using a simple model of unstable spiral and justified numerically for two unidirectionally coupled chaotic Rössler systems. The maximum prediction time attained with our algorithm equals to the half of characteristic period of chaotic oscillations.
Keywords: synchronization, delay, anticipating of chaos
PACS: 05.45.Xt, 05.45.Gg, 02.30.Yy


CHAOTINIŲ BŪSENŲ PROGNOZĖ NAUDOJANT PRIEŠINGOS FAZĖS RYŠĮ
T. Pyragienė, K. Pyragas
Fizinių ir technologijos mokslų centro Puslaidininkių fizikos institutas, Vilnius, Lietuva

Nagrinėjama prognozuojanti sinchronizacija [3]. Toks sinchronizacijos režimas stebimas siųstuvo–imtuvo konfigūracijoje, kai siųstuvas veikia imtuvą, o atvirkštinio ryšio nėra. Imtuvas sinchronizuojasi su siųstuvu ateitimi, t. y. imtuvas numato siųstuvo dinamikos ateitį. Chaotinių sistemų prognozės uždaviniuose siekiama gauti kiek įmanoma ilgesnę prognozės trukmę. Atlikti tyrimai parodė, kad paprastai naudojama diagonali matrica yra neefektyvi [3], nes šiuo atveju maksimali prognozės trukmė žymiai mažesnė už būdingąsias dinaminės sistemos trukmes. Neseniai pasiūlėme nediagonalia ˛ ryšio matricą, kurios konstravimo algoritmas paremtas fazės delsos kompensacija (FDK) imtuvo sistemoje [23]. Šis metodas žymiai prailgina prognozės trukmę tiek, kad ji tampa palyginama su būdinguoju chaotinės sistemos periodu.
Darbe siūlomas modifikuotas FDK algoritmas: imtuvo sistemoje uždelstas grįžtamasis ryšys įjungiamas priešfazėje. Ši modifikacija žymiai supaprastina prognozuojančios sinchronizacijos režimo eksperimentinį įgyvendinimą. Pasiūlyto algoritmo atveju prognozės trukmė yra lygi charakteringo chaotinės sistemos periodo pusei.


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