article · International Journal of Bifurcation and Chaos
This research investigates the occurrence of intermittent extreme events within a four-dimensional autonomous hyperchaotic system that lacks equilibria. Traditionally, extreme events are linked to instabilities arising from equilibrium points, but this study demonstrates that such events can emerge even in their complete absence. Numerical simulations show sudden, large-amplitude bursts from otherwise bounded chaotic oscillations. These events are characterised by an amplitude distribution with a heavy tail, accurately described by a Fréchet-type Generalised Extreme Value distribution. The time between events follows an exponential distribution, indicating they are statistically uncorrelated. The study also found that these extreme events are robust, persisting across wide parameter ranges of both chaotic and hyperchaotic dynamics. This work expands the fundamental understanding of how rare, large-amplitude events can be generated in complex systems.
Understanding how extreme events arise in complex systems is crucial for predicting and mitigating their impact. This research shows that such events can occur in a wider range of systems than previously thought, even without traditional equilibrium-based instabilities. This fundamental insight could inform future studies on unpredictable phenomena in various fields.
The abstract describes fundamental research into the generation of extreme events in complex dynamical systems. It does not indicate any specific application pathways, potential users, or a readiness level for commercialisation. This work primarily contributes to theoretical understanding.
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This paper reveals the occurrence of intermittent extreme events in a four-dimensional autonomous hyperchaotic system without equilibria. In the absence of equilibria, classical mechanisms based on saddle structures and Shilnikov-type analysis cannot be invoked, raising the fundamental question of whether extreme events can arise without equilibrium-based instabilities. Through numerical simulations, we demonstrate that the system exhibits sudden transitions from bounded chaotic oscillations to rare, large-amplitude bursts. Extreme events are identified using a threshold defined as the mean plus four standard deviations of the local-maxima time series. The amplitude distribution exhibits a pronounced heavy tail and is well described by a Generalized Extreme Value (GEV) distribution of Fréchet type, with shape parameter [Formula: see text] (95% confidence interval [Formula: see text], validated by parametric bootstrap), which remains stable when the threshold multiplier is varied from 3.5 to 5.0. The inter-event intervals follow an exponential distribution, indicating that successive events are statistically uncorrelated and consistent with a Poisson process. A two-dimensional parameter analysis reveals that extreme events persist across broad regions spanning both chaotic and hyperchaotic dynamics. An offset boosting analysis shows that the variable [Formula: see text] is boostable, translating the attractor rigidly along the [Formula: see text]-axis without altering the dynamical complexity of the system; a multistability diagnostic reveals no coexisting attractors along the scanned family of initial conditions at the reference parameter set. These results demonstrate that extreme events can arise in the complete absence of equilibria, thereby extending the current understanding of rare-event generation beyond equilibrium-based dynamical scenarios. To the best of our knowledge, this constitutes the first numerical evidence of extreme events in a hyperchaotic system without equilibria.
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DOI: 10.1142/s0218127426502299
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