Tnx a lot for your work . Science 264, 70–72. J. Atmos. Fractal geometry: what is it, and what does it do? *Correspondence: Olusegun S. A. Oluwole,, Front. Phys. doi: 10.1111/j.1600-0870.2010.00482.x, An, S., and Wang, B. You don't want that code. Trajectories of dissipative systems return to a region of phase space called attractor as time t → ∞. Hurst spectra of multifractal detrended fluctuation analysis show that annual oscillatory components of ENSO and influenza in five regions of the study are multifractals. (E) Oceania. The virulent H3N2 influenza virus, which circulated during the moderately severe seasons of 2007–2008 and the mild season of 2011–2012 (Bresee and Hayden, 2013), show that virulence is not the only determinant of severity. Synchronization of chaotic oscillators occurs when a property of their motion, like phase or amplitude, adjusts to common behavior due to coupling or forcing such that their trajectories evolve in a common phase (Boccaletti et al., 2002). (D–F) Oceania. And this is the Numerical Calculation of Lyapunov Exponent. The cross correlation between P1(τ) and P2(τ) is defined as CPR=〈P-1(τ)P-2(τ)〉/(σ1σ2). Choose a web site to get translated content where available and see local events and offers. (1969). Ellner S. Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data[J].Phys Lett A, 1991,153: 357–363. The geometry of phase space attractors characterizes dynamic systems. Sci. Environ. Commum. Adv. (excuse my English), If you have questions, PLEASE DON'T POST THEM HERE. Mazzarella, A., and Giuliacci, A. Although influenza epidemics peak during the winter, the period of increase occurrence of influenza range from October to April in northern hemisphere and from May to November in the southern hemisphere, which is fall to spring in both hemispheres. A Matlab version of the Lyapunov exponent estimation algorithm of Wolf et al. In Physica 16D (1985) we presented an algorithm that estimates the dominant Lyapunov exponent of a 1-D time series by monitoring orbital divergence. MathWorks is the leading developer of mathematical computing software for engineers and scientists. Sci. Strong coupling of instantaneous amplitudes and frequencies of ENSO and influenza annual oscillatory components indicate coherence of amplitude and frequency modulations. The geometry of chaotic dynamics - a complex network perspective. Determining Lyapunov exponents from a time series. Since the maximum Lyapunov exponents of annual oscillatory components of ENSO and influenza are positive, the attractors of both dynamics have fractal dimensions, which indicate chaos. and in that way I get the maximum exposure of lyapunov? Wolf Lyapunov exponent estimation from a time series. correlation dimension. Lond. Genesis and evolution of the 1997-98 El Nino. but i have a question : how can i find the result of Lyapunov Exponent from your code? (D) Asia. Phys. McPhaden, M. J. Although the power of ENSO spectra is strong in multiple bandwidths from sub-annual to multi-decadal periodicities, that of influenza is strong in the bandwidth about 1 year periodicity except for Asia region, which has strong sub-annual to multi-decadal oscillatory components (Figures 4A–F). An output file is created when the program is run. Metrics of network analysis, which maps time series to networks with distinct topological characteristics (Campanharo et al., 2011), have been used to detect the presence of regimes in dynamic systems. I am unable to run the program. These metrics, which complement visual interpretation of recurrence plots, are measures of complexities that are derived from diagonal and vertical structures of recurrence plots (Marwan et al., 2002, 2007).

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