A Real-World Application of Chaos Theory

Topic Information

Dear Colleagues,

Chaos theory is one of the most elegant theories in mathematics which deals with how small changes in initial conditions can lead to vastly different outcomes in complex systems, making long-term predictions difficult. Several different techniques are used to predict the chaos in a dynamical system, some of which are sensitivity, phase portraits, bifurcation theory, Lyapunov exponents, etc. Each of these techniques helps mathematicians analyze problems more deeply.

Topics of Interest include, but are not limited to, the following:

• (i) Bifurcation analysis;
• (ii) multi-stability analysis;
• (iii) sensitivity analysis;
• (iv) Lyapunov exponents;
• (v) attractors;
• (vi) basin theory;
• (vii) Poincare map.

Dr. Adil Jhangeer
Dr. Mudassar Imran
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AppliedMath appliedmath	0.7	1.1	2021	23.5 Days	CHF 1200	Submit
Axioms axioms	1.6	-	2012	21.6 Days	CHF 2400	Submit
Computation computation	1.9	4.1	2013	16.7 Days	CHF 1800	Submit
Mathematics mathematics	2.2	4.6	2013	18.4 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.3	2009	17.1 Days	CHF 2400	Submit

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Published Papers (3 papers)

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All AppliedMath Axioms Computation Mathematics Symmetry

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17 pages, 7815 KiB  

Open AccessArticle

Design and Analysis of Memristive Electromagnetic Radiation in a Hopfield Neural Network

by Zhimin Gu, Bin Hu, Hongxin Zhang, Xiaodan Wang, Yaning Qi and Min Yang

Symmetry 2025, 17(8), 1352; https://doi.org/10.3390/sym17081352 - 19 Aug 2025

Viewed by 216

Abstract

This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive [...] Read more.

This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive nonlinear analysis. Numerical investigations demonstrate that memristor-induced electromagnetic effects induce distinctive phenomena, including coexisting attractors, transient chaotic states, symmetric bifurcation diagrams and attractor structures, and constant chaos. The proposed system can generate more than 12 different attractors and extends the chaotic region. Compared with the chaotic range of the baseline Hopfield neural network (HNN), the expansion amplitude reaches 933%. Dynamic characteristics are systematically examined using phase trajectory analysis, bifurcation mapping, and Lyapunov exponent quantification. Experimental validation via a DSP-based hardware implementation confirms the model’s operational feasibility and consistency with numerical predictions, establishing a reliable platform for electromagnetic–neural interaction studies. Full article

(This article belongs to the Topic A Real-World Application of Chaos Theory)

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25 pages, 6742 KiB  

Open AccessArticle

Reservoir Computing with a Single Oscillating Gas Bubble: Emphasizing the Chaotic Regime

by Hend Abdel-Ghani, A. H. Abbas and Ivan S. Maksymov

AppliedMath 2025, 5(3), 101; https://doi.org/10.3390/appliedmath5030101 - 7 Aug 2025

Viewed by 219

Abstract

The rising computational and energy demands of artificial intelligence systems urge the exploration of alternative software and hardware solutions that exploit physical effects for computation. According to machine learning theory, a neural network-based computational system must exhibit nonlinearity to effectively model complex patterns [...] Read more.

The rising computational and energy demands of artificial intelligence systems urge the exploration of alternative software and hardware solutions that exploit physical effects for computation. According to machine learning theory, a neural network-based computational system must exhibit nonlinearity to effectively model complex patterns and relationships. This requirement has driven extensive research into various nonlinear physical systems to enhance the performance of neural networks. In this paper, we propose and theoretically validate a reservoir-computing system based on a single bubble trapped within a bulk of liquid. By applying an external acoustic pressure wave to both encode input information and excite the complex nonlinear dynamics, we showcase the ability of this single-bubble reservoir-computing system to forecast a Hénon benchmarking time series and undertake classification tasks with high accuracy. Specifically, we demonstrate that a chaotic physical regime of bubble oscillation—where tiny differences in initial conditions lead to wildly different outcomes, making the system unpredictable despite following clear rules, yet still suitable for accurate computations—proves to be the most effective for such tasks. Full article

(This article belongs to the Topic A Real-World Application of Chaos Theory)

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24 pages, 1751 KiB  

Open AccessArticle

Chaotic-Based Shellcode Encryption: A New Strategy for Bypassing Antivirus Mechanisms

by Gang-Cheng Huang, Ko-Chin Chang and Tai-Hung Lai

Symmetry 2024, 16(11), 1526; https://doi.org/10.3390/sym16111526 - 14 Nov 2024

Cited by 1 | Viewed by 3897

Abstract

This study employed chaotic systems as an innovative approach for shellcode obfuscation to evade current antivirus detection methods. Standard AV solutions primarily rely on static signatures and heuristic analysis to identify malicious code. However, chaotic systems employ dynamic and unpredictable encryption methods, significantly [...] Read more.

This study employed chaotic systems as an innovative approach for shellcode obfuscation to evade current antivirus detection methods. Standard AV solutions primarily rely on static signatures and heuristic analysis to identify malicious code. However, chaotic systems employ dynamic and unpredictable encryption methods, significantly obstructing detection efforts. The utilization of various chaotic maps for shellcode encryption facilitates the generation of multiple unique variations from the same functional code, each exhibiting distinct unpredictability due to the inherent nonlinearity and sensitivity of chaotic systems to initial conditions. The unpredictability of these situations poses a considerable challenge for antivirus software in recognizing consistent patterns, resulting in decreased detection rates. The findings from our experiments demonstrate that chaos-driven encryption methods significantly outperform traditional encryption techniques in terms of evading detection. This paper emphasizes the potential of chaos theory to enhance malware evasion strategies, offering a sophisticated approach to bypassing modern antivirus protections while ensuring the effectiveness of malicious payloads. Full article

(This article belongs to the Topic A Real-World Application of Chaos Theory)

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