title: Characterization of the chaos-hyperchaos transition based on return times.
abstract: We discuss the problem of the detection of hyperchaotic oscillations in coupled nonlinear systems when the available information about this complex dynamical regime is very limited. We demonstrate the ability of diagnosing the chaos-hyperchaos transition from return times into a Poincaré section and show that an appropriate selection of the secant plane allows a correct estimation of two positive Lyapunov exponents (LEs) from even a single sequence of return times. We propose a generalized approach for extracting dynamics from point processes that allows avoiding spurious identification of the dynamical regime caused by artifacts. The estimated LEs are nearly close to their expected values if the second positive LE is essentially different from the largest one. If both exponents become nearly close, an underestimation of the second LE may be obtained. Nevertheless, distinctions between chaotic and hyperchaotic regimes are clearly possible.
authors.affiliation: Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia.|Saratov State Technical University, Politehnicheskaya Str. 77, 410054, Saratov, Russia.
authors.forename: A N
authors.initials: AN
authors.lastname: Pavlov
authors.affiliation: Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia.
authors.forename: O N
authors.initials: ON
authors.lastname: Pavlova
authors.affiliation: Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia.|Tikrit University Salahudin, Tikrit Qadisiyah, University Str., PO Box 42, Tikrit, Iraq.
authors.forename: Y K
authors.initials: YK
authors.lastname: Mohammad
authors.affiliation: Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany.|Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany.
authors.forename: J
authors.initials: J
authors.lastname: Kurths