000056288 001__ 56288
000056288 005__ 20200221144246.0
000056288 0247_ $$2doi$$a10.1137/15M1039201
000056288 0248_ $$2sideral$$a94770
000056288 037__ $$aART-2016-94770
000056288 041__ $$aeng
000056288 100__ $$aWilczak, D.
000056288 245__ $$aCoexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: A computer-assisted proof
000056288 260__ $$c2016
000056288 5060_ $$aAccess copy available to the general public$$fUnrestricted
000056288 5203_ $$aIt has recently been reported P. C. Reich, Neurocomputing, 74 (2011), pp. 3361-3364] that it is quite difficult to distinguish between chaos and hyperchaos in numerical simulations which are frequently "noisy." For the classical four-dimensional (4D) Rössler model O. E. Rössler, Phys. Lett. A, 71 (1979), pp. 155-157] we show that the coexistence of two invariant sets with different nature (a global hyperchaotic invariant set and a chaotic attractor) and heteroclinic connections between them give rise to long hyperchaotic transient behavior, and therefore it provides a mechanism for noisy simulations. The same phenomena is expected in other 4D and higher-dimensional systems. The proof combines topological and smooth methods with rigorous numerical computations. The existence of (hyper)chaotic sets is proved by the method of covering relations P. Zgliczynski and M. Gidea, J. Differential Equations, 202 (2004), pp. 32-58]. We extend this method to the case of a nonincreasing number of unstable directions which is necessary to study hyperchaos to chaos transport. The cone condition H. Kokubu, D. Wilczak, and P. Zgliczynski, Nonlinearity, 20 (2007), pp. 2147-2174] is used to prove the existence of homoclinic and heteroclinic orbits between some periodic orbits which belong to both hyperchaotic and chaotic invariant sets. In particular, the existence of a countable infinity of heteroclinic orbits linking hyperchaos with chaos justifies the presence of long transient behavior.
000056288 536__ $$9info:eu-repo/grantAgreement/ES/UZ/CUD2015-CIE-05$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2015-64095-P$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883$$9info:eu-repo/grantAgreement/ES/DGA/E48
000056288 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000056288 590__ $$a1.761$$b2016
000056288 591__ $$aMATHEMATICS, APPLIED$$b34 / 255 = 0.133$$c2016$$dQ1$$eT1
000056288 591__ $$aPHYSICS, MATHEMATICAL$$b16 / 55 = 0.291$$c2016$$dQ2$$eT1
000056288 592__ $$a1.288$$b2016
000056288 593__ $$aModeling and Simulation$$c2016$$dQ1
000056288 593__ $$aAnalysis$$c2016$$dQ1
000056288 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000056288 700__ $$0(orcid)0000-0002-5701-1670$$aSerrano, S.$$uUniversidad de Zaragoza
000056288 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, R.$$uUniversidad de Zaragoza
000056288 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000056288 773__ $$g15, 1 (2016), 356-390$$pSIAM J. Appl. Dyn. Syst.$$tSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS$$x1536-0040
000056288 8564_ $$s8375319$$uhttps://zaguan.unizar.es/record/56288/files/texto_completo.pdf$$yVersión publicada
000056288 8564_ $$s89725$$uhttps://zaguan.unizar.es/record/56288/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000056288 909CO $$ooai:zaguan.unizar.es:56288$$particulos$$pdriver
000056288 951__ $$a2020-02-21-13:25:20
000056288 980__ $$aARTICLE