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7 articles for “Chaotic dynamics”
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A Novel Mathematical Exploration of Fractal Dynamics in Hyperbolic Spaces
Abstract: This research paper presents an original study on the behavior, generation, and properties of fractal structures within hyperbolic geometry. Unlike classical Euclidean fractals, hyperbolic fractals demonstrate accelerated boundary complexity and distinct scaling symmetries due to the curvature of the underlying space. The paper proposes new iterative models, analyzes geometric invariants, and explores potential applications in data visualization, network science, and theoretical physics. This research paper conducts an in-depth investigation into …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 1–7 Read article
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Symmetry Breaking in Mathematical Models: Bifurcation, Chaos, and Pattern Formation
Abstract: Symmetry breaking serves as a central organizing principle in the understanding of nonlinear systems across physics, biology, chemistry, and engineering. When a system transitions from a symmetric state to an asymmetric configuration, it often signals the onset of new structures, dynamic behaviors, or even chaotic regimes. This review explores symmetry breaking from the theoretical and mathematical perspectives of bifurcation theory, chaos theory, and pattern formation. We discuss how small parameter …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 25–30 Read article
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Key Generation Algorithms Using Difference Equations with Multi-Precision Arithmetic: A Review
Abstract: Modern cryptographic systems rely on robust key generation to secure data and communication. This review explores the integration of difference equations and multi-precision arithmetic for cryptographic key generation, addressing limitations in traditional methods like pseudorandom number generators and chaotic systems. Difference equations produce deterministic yet chaotic sequences ideal for cryptography due to their sensitivity to initial conditions and nonlinearity. However, finite precision arithmetic can lead to periodicity and loss of …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 23–36 Read article
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Spatiotemporal Analysis of Mean-Field Coupled Lorenz Oscillators for Applications in Electronic Network Design and Chaotic Synchronization
Abstract: This study investigates the spatiotemporal behavior of a network of 100 coupled Lorenz oscillators interacting through mean-field coupling with coupling strength κ = 0.1 and explores its relevance to electronic system design and nonlinear network architectures. While each oscillator follows classical Lorenz dynamics, the coupling mechanism enables collective behavior that resembles synchronization phenomena observed in distributed electronic and communication systems. Numerical simulations reveal rich dynamical characteristics including partial synchronization, emergent …
Published in Journal of Electronic Design Technology · Vol. 17, Issue 2, 2026 Read article
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Noise-Driven Collective Behavior in Mean-Field Coupled Lorenz Oscillator Networks
Abstract: This work investigates the spatiotemporal dynamics of an ensemble of 100 identical Lorenz oscillators coupled through a mean-field scheme in the presence of additive noise. Building on prior studies of spatiotemporal chaos in coupled Lorenz arrays and mean-field coupled chaotic oscillators, the focus is on how the competition between deterministic coupling and stochastic forcing shapes collective behavior, including complete synchronization, desynchronization, clustered states, and noise-modified spatiotemporal chaos. The governing equations …
Published in International Journal of Advanced Control and System Engineering · Vol. 4, Issue 2, 2026 Read article
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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Advances in Pipe Flow Systems, Turbulence, and Combustion Processes in Fluid Mechanics
Abstract: Fluid mechanics plays a critical role in the design and optimization of engineering systems involving fluid transport, energy conversion, and thermal processes. This review presents recent advances in pipe flow systems, turbulence behavior, and combustion processes, highlighting their interdependence in modern applications. Pipe flow systems are essential in industries such as water distribution, oil and gas transport, and chemical processing, where flow characteristics are influenced by factors such as pressure, …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 1, 2026 · pp. 1–7 Read article