Essay on Kolmogorov Law of Minus 5 over 3 Viewed with Golden Ratio

Li, Ming; Zhao, Wei

doi:10.1155/2013/680678

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…We should give further study in our future work. The basic concept of the golden ratio is given in [11][12][13] and [14] for the spectra used in [11,12]. .…”

Section: Numerical Simulationmentioning

confidence: 99%

Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Peng

Kurths

et al. 2013

Mathematical Problems in Engineering

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Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.

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“…We should give further study in our future work. The basic concept of the golden ratio is given in [11][12][13] and [14] for the spectra used in [11,12]. .…”

Section: Numerical Simulationmentioning

confidence: 99%

Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Peng

Kurths

et al. 2013

Mathematical Problems in Engineering

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Noise or Random Fluctuations in Physical Systems: A Review

Selvam

2017

Springer Atmospheric Sciences

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Self-organized Criticality: A Signature of Quantum-like Chaos in Atmospheric Flows

Selvam

2017

Springer Atmospheric Sciences

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Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all spacetime scales ranging from turbulence (centimetres-seconds) to climate (kilometres-years). Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. Mathematical models for simulation and prediction of atmospheric flows are nonlinear and do not possess analytical solutions. Finite precision computer realizations of nonlinear models give unrealistic solutions because of deterministic chaos, a direct consequence of round-off error growth in iterative numerical computations. Recent studies show that round-off error doubles on an average for each iteration of iterative computations. Round-off error propagates to the mainstream computation and gives unrealistic solutions in numerical weather prediction (NWP) and climate models, which incorporate thousands of iterative computations in longterm numerical integration schemes. An alternative non-deterministic cell dynamical system model for atmospheric flows developed by the author predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics. The model provides universal quantification for self-organized criticality in terms of the statistical normal distribution. Model predictions are in agreement with a majority of observed spectra of time series of several standard climatological data sets representative of disparate climatic regimes. Universal spectrum for natural climate variability rules out linear trends. Man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change. Model concepts, if correct, rule out unambiguously, linear trends in climate. Climate change will only be manifested as increase or decrease in the natural variability. However, more stringent tests of model concepts and predictions are required before applications to such an important issue as climate change. The cell dynamical system model for atmospheric flows is a general systems theory applicable in general to all dynamical systems in other fields of science, such as, number theory, biology, physics and botany.

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Essay on Kolmogorov Law of Minus 5 over 3 Viewed with Golden Ratio

Cited by 4 publications

References 24 publications

Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Noise or Random Fluctuations in Physical Systems: A Review

Self-organized Criticality: A Signature of Quantum-like Chaos in Atmospheric Flows

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