Extracting Chaos Control Parameters from Time Series Analysis

Santos, R.B.B.; Graves, Julio Cesar

doi:10.1088/1742-6596/285/1/012002

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…In our future work, we plan to study the specific characteristics of systems that exhibit stable, oscillatory, or unstable behaviour and to understand what this means in terms of the ways that tokens are introduced in these systems. In the case of chaotic behaviour, control parameters can be identified [43,44], and if it turns out that tokens do have this influence, they can be seen as a stabilising factor in tokenised economic systems.…”

Section: Discussionmentioning

confidence: 99%

A Chemical Analysis of Hybrid Economic Systems—Tokens and Money

Pardi¹,

Paolucci

2021

Mathematics

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With the influence of digital technology in our daily lives continuously growing, we investigate methods with the purpose of assessing the stability, sustainability, and design of systems of token economies that include tokens and conventional currencies. Based on a chemical approach, we model markets with a minimum number of variables and compare the transaction rates, stability, and token design properties at different levels of tokenisation. The kinetic study reveals that in certain conditions, if the price of a product contains both conventional money and tokens, one can treat this combination as one composite currency. The dynamic behaviour of the analysed systems is proven to be dynamically stable for the chosen models. Moreover, by applying the supply and demand law to recalculate the prices of products, the necessity of previous knowledge of certain token attributes—token divisibility and token–money exchange rates—emerges. The chemical framework, along with the analytic methods that we propose, is flexible enough to be adjusted to a variety of conditions and offer valuable information about economic systems.

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Section: Discussionmentioning

confidence: 99%

A Chemical Analysis of Hybrid Economic Systems—Tokens and Money

Pardi¹,

Paolucci

2021

Mathematics

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“…Applications of chaos control techniques [2,3] in neural dynamics, mainly due to its possible medical applications in the treatment of epilepsy [4], have also been explored for some time. A number of anticontrol of chaos methods have also been developed for this purpose [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…Chaos control-a method for maintaining periodic dynamics in chaotic systems-has received considerable attention following successful experimental demonstration in physical, chemical and biological systems [1]. Applications of chaos control techniques [2,3] in neural dynamics, mainly due to its possible medical applications in the treatment of epilepsy [4], have also been explored for some time. A number of anticontrol of chaos methods have also been developed for this purpose [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Reliability of unstable periodic orbit based control strategies in biological systems

Mishra

Hasse

Biswal

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information from the detected UPO trajectories are vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics. Unstable periodic orbits (UPOs) analysis has now become an established tool for detecting determinism in biological systems. If the system is truly deterministic, accurate UPO characteristics can be further used for application of control or anti control strategies with potential medical application. However, accurate biological time series analysis for UPOs critically depend on the length of data set, strength of noise, type of geometry, nonstationarity etc. In this work we show that it is possible to establish determinism through UPO analysis in presence of all these factors. However, the inaccuracy in the measured UPO parameters and non-stationarity nature of biological systems mean only adaptive control strategies are useful for successful chaos control in such systems. At the same time, comparable success of adaptive control strategies on a stochastic neural network model of epileptic slices demand more stringent criteria for linking adaptive control success with determinism.

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Extracting Chaos Control Parameters from Time Series Analysis

Cited by 2 publications

References 11 publications

A Chemical Analysis of Hybrid Economic Systems—Tokens and Money

A Chemical Analysis of Hybrid Economic Systems—Tokens and Money

Reliability of unstable periodic orbit based control strategies in biological systems

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