Overview and Perspectives of Chaos Theory and Its Applications in Economics

Fernández-Díaz, Andrés

doi:10.3390/math12010092

Cited by 8 publications

(2 citation statements)

References 27 publications

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“…This phenomenon, known as chaos, arises in nonlinear systems and is characterized by extreme sensitivity to initial conditions, often leading to the iconic "butterfly effect". Chaotic dynamics are remarkably pervasive, manifesting in diverse domains such as social, biological, and technical systems [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A Deterministic Chaos-Model-Based Gaussian Noise Generator

Haliuk,

Vovchuk,

Spinazzola

et al. 2024

Electronics

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The abilities of quantitative description of noise are restricted due to its origin, and only statistical and spectral analysis methods can be applied, while an exact time evolution cannot be defined or predicted. This emphasizes the challenges faced in many applications, including communication systems, where noise can play, on the one hand, a vital role in impacting the signal-to-noise ratio, but possesses, on the other hand, unique properties such as an infinite entropy (infinite information capacity), an exponentially decaying correlation function, and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window, putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criterion on which the main idea of this study is based on is the central limit theorem, which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. This study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.), whose output signals are analyzed according to criteria that encompass the probability density functions of the chaotic signal itself, its envelope, and its phase and statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. Thus, a statistical-characteristic-based algorithm, which includes a series of tests, was developed for a Gaussian-like signal assessment. Following the algorithm, the analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates a Gaussian distribution. This allows for the generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

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Section: Introductionmentioning

confidence: 99%

A Deterministic Chaos-Model-Based Gaussian Noise Generator

Haliuk,

Vovchuk,

Spinazzola

et al. 2024

Electronics

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Deterministic chaos models-based Gaussian noise generator

Haliuk,

Vovchuk,

Spinazzola

et al. 2024

Preprint

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The abilities of quantitative description of noise are restricted due to its origin and only the statistical and spectral analysis methods can be applied while an exact time evolution cannot be defined or predicted. It emphasizes the challenges faced in many applications including communication systems where noise can play, on one hand, a vital role impacting signal-to-noise ratio but possessing, on the other hand, unique properties such as infinite entropy (infinite information capacity), exponentially decaying correlation function and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criteria, on which the main idea of the study is based on, is the Central Limit Theorem which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. The study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.) whose output signals are analyzed according to criteria that encompass the probability density functions of a chaotic signal itself and its envelope and phase, statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. The analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates Gaussian distribution. It allows generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

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Free Will as Defined by the Constrained Disorder Principle: a Restricted, Mandatory, Personalized, Regulated Process for Decision-Making

Ilan

2024

Integr. psych. behav.

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The concept of free will has challenged physicists, biologists, philosophers, and other professionals for decades. The constrained disorder principle (CDP) is a fundamental law that defines systems according to their inherent variability. It provides mechanisms for adapting to dynamic environments. This work examines the CDP's perspective of free will concerning various free will theories. Per the CDP, systems lack intentions, and the "freedom" to select and act is built into their design. The "freedom" is embedded within the response range determined by the boundaries of the systems' variability. This built-in and self-generating mechanism enables systems to cope with perturbations. According to the CDP, neither dualism nor an unknown metaphysical apparatus dictates choices. Brain variability facilitates cognitive adaptation to complex, unpredictable situations across various environments. Human behaviors and decisions reflect an underlying physical variability in the brain and other organs for dealing with unpredictable noises. Choices are not predetermined but reflect the ongoing adaptation processes to dynamic prssu½res. Malfunctions and disease states are characterized by inappropriate variability, reflecting an inability to respond adequately to perturbations. Incorporating CDP-based interventions can overcome malfunctions and disease states and improve decision processes. CDP-based second-generation artificial intelligence platforms improve interventions and are being evaluated to augment personal development, wellness, and health.

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Overview and Perspectives of Chaos Theory and Its Applications in Economics

Cited by 8 publications

References 27 publications

A Deterministic Chaos-Model-Based Gaussian Noise Generator

A Deterministic Chaos-Model-Based Gaussian Noise Generator

Deterministic chaos models-based Gaussian noise generator

Free Will as Defined by the Constrained Disorder Principle: a Restricted, Mandatory, Personalized, Regulated Process for Decision-Making

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