Search Results (354)

This study investigates a modified five-dimensional chaotic system by incorporating structural term adjustments and Caputo fractional-order differential operators. The modified system exhibits significantly enriched dynamic behaviors, including offset boosting, phase trajectory rotation, phase trajectory reversal, and contraction phenomena. Additionally, the system exhibits bidirectional transitions—conservative-to-dissipative transitions governed by initial conditions and dissipative-to-conservative transitions controlled by fractional order variations—along with a unique chaotic-to-quasiperiodic transition observed exclusively at low fractional orders. To validate the system’s physical realizability, a signal processing platform based on Digital Signal Processing (DSP) is implemented. Experimental measurements closely align with numerical simulations, confirming the system’s feasibility for practical applications. Full article

Stacking fault tetrahedra (SFTs) are typically considered improbable in high stacking fault energy metals like aluminum. Using molecular statics and dynamics simulations, we reveal the formation, growth, and transformation of SFTs in aluminum via vacancy aggregation. Three types—perfect, truncated, and defective SFTs—are characterized by their structure, formation energy, and binding energy across a range of vacancy cluster sizes. Formation energies of perfect and truncated SFTs follow a scaling relation; beyond a critical size, truncated SFTs become thermodynamically favored, indicating a size-dependent transformation pathway. Binding energy and structure evolution exhibit quasi-periodic behavior, where vacancies initially adsorb at the vertices or the midpoints of the edges of a perfect SFT, then aggregate along one facet, triggering fault nucleation and a binding energy jump as the system reconstructs into a new perfect SFT. Molecular dynamics simulations further confirm the SFT nucleation and growth via vacancy aggregation, consistent with thermodynamic predictions. SFTs exhibit notable thermal mobility, enabling coalescence and evolution into vacancy-type dislocation loops. BCC-like $V_5$ clusters are identified as potential nucleation precursors. These findings explain the nanoscale, low-temperature nature of SFTs in aluminum and offer new insights into defect evolution and control in FCC metals. Full article

In this research paper, we study symmetry groups, soliton solutions, and the dynamical behavior of the Ivancevic Option Pricing Model (IOPM). First, we find the Lie symmetries of the considered model; next, we use them to determine the corresponding symmetry groups. Then, we attempt to solve IOPM by means of two methods. We provide some wave solutions and give further details of the solution using 2D and 3D graphs. These results are interpreted as important clarifications in financial mathematics and deepen our understanding of the dynamics involved during the pricing of options. Secondly, the quasi-periodic behavior of the two-dimensional dynamical system and its perturbed system are plotted using Python software (Python 3.13.5 version). Various frequencies and amplitudes are considered to confirm the quasi-periodic behavior via the Lyapunov exponent, bifurcation diagram, and multistability analysis. These findings are particularly in consonance with current research that investigates IOPM as a nonlinear wave alternate for normal models and the importance of graphical representations in the understanding of financial derivative dynamics. We, therefore, hope to fill in the gaps in the literature that currently exist about the use of multi-solution methods and their effects on financial modeling through the employment of sophisticated graphical techniques. This will be helpful in discussing matters in the field of financial mathematics and open up new directions of investigation. Full article

This study explores analytical soliton solutions for the cubic–quintic time-fractional nonlinear non-paraxial pulse transmission model. This versatile model finds numerous uses in fiber optic communication, nonlinear optics, and optical signal processing. The strength of the quintic and cubic nonlinear components plays a crucial role in nonlinear processes, such as self-phase modulation, self-focusing, and wave combining. The fractional nonlinear Schrödinger equation (FNLSE) facilitates precise control over the dynamic properties of optical solitons. Exact and methodical solutions include those involving trigonometric functions, Jacobian elliptical functions (JEFs), and the transformation of JEFs into solitary wave (SW) solutions. This study reveals that various soliton solutions, such as periodic, rational, kink, and SW solitons, are identified using the complete discrimination polynomial methods (CDSPM). The concepts of chaos and bifurcation serve as the framework for investigating the system qualitatively. We explore various techniques for detecting chaos, including three-dimensional and two-dimensional graphs, time-series analysis, and Poincarè maps. A sensitivity analysis is performed utilizing a variety of initial conditions. Full article

Inertial instability is a key process in the dynamics of rotating and stratified fluids, which arises when the absolute vorticity of the flow becomes negative. This study explored the nonlinear behavior of inertial instability by incorporating a hidden symmetry into the equations of motion governing atmospheric dynamics. The atmosphere was modeled as a complex system composed of interacting structural elements, each capable of oscillatory motion influenced by planetary rotation and geostrophic shear. By applying a symmetry-based framework rooted in projective geometry and Riccati-type transformations, we show that synchronization and structural coherence can emerge spontaneously, independent of external forcing. This hidden symmetry leads to rich dynamical behavior, including phase coupling, quasi-periodicity, and bifurcations. Our results suggest that inertial instability, beyond its classical linear interpretation, may play a significant role in organizing large-scale atmospheric patterns through internal geometric constraints. Full article

TXS 0506+056 is a blazar associated with neutrino events. The study on its variation mechanics and periodicity analysis is meaningful to understand other BL Lac objects. The local cross-correlation function (LCCF) analysis presents a 3$\sigma$ correlation in both the $\gamma$-ray versus optical and optical versus radio light curves. The time lag analysis suggests that the optical and $\gamma$-ray band share the same emission region, located upstream of the radio band in the jet. We use both the weighted wavelet Z-transform and generalized Lomb–Scargle methods to analyze the periodicity. We find two plausible quasi-periodic oscillations (QPOs) at ${506}_{-56}^{+133}$ days and ${175}_{-7}^{+15}$ days for the light curve of the optical band. For the $\gamma$-ray band, we find that the spectrum varies with the softer when brighter (SWB) trend, which could be explained naturally if a stable very high energy component exists. For the optical band, TXS 0506+056 exhibits a harder when brighter (HWB) trend. We discover a trend transition from HWB to SWB in the X-ray band, which could be modeled by the shift in peak frequency assuming that the X-ray emission is composed of the synchrotron and the inverse Compton (IC) components. The flux correlations of $\gamma$-ray and optical bands behave anomalously during the period of neutrino events, indicating that there are possible other hadronic components associated with neutrino. Full article

Despite its significance, hysteresis remains underrepresented in mainstream models of plasticity. In this work, we propose a novel framework that explicitly models hysteresis in simple one- and two-neuron models. Our models capture key feedback-dependent phenomena such as bistability, multistability, periodicity, quasi-periodicity, and chaos, offering a more accurate and general representation of neural adaptation. This opens the door to new insights in computational neuroscience and neuromorphic system design. Synaptic weights change in several contexts or mechanisms including, Bienenstock–Cooper–Munro (BCM) synaptic modification, where synaptic changes depend on the level of post-synaptic activity; homeostatic plasticity, where all of a neuron synapses simultaneously scale up or down to maintain stability; metaplasticity, or plasticity of plasticity; neuromodulation, where neurotransmitters influence synaptic weights; developmental processes, where synaptic connections are actively formed, pruned and refined; disease or injury; for example, neurological conditions can induce maladaptive synaptic changes; spike-time dependent plasticity (STDP), where changes depend on the precise timing of pre- and postsynaptic spikes; and structural plasticity, where changes in dendritic spines and axonal boutons can alter synaptic strength. The ability of synapses and neurons to change in response to activity is fundamental to learning, memory formation, and cognitive adaptation. This paper presents simple continuous and discrete neuro-modules with adapting feedback synapses which in turn are subject to feedback. The dynamics of continuous periodically driven Hopfield neural networks with adapting synapses have been investigated since the 1990s in terms of periodicity and chaotic behaviors. For the first time, one- and two-neuron models are considered as parameters are varied using a feedback mechanism which more accurately represents real-world simulation, as explained earlier. It is shown that these models are history dependent. A simple discrete two-neuron model with adapting feedback synapses is analyzed in terms of stability and bifurcation diagrams are plotted as parameters are increased and decreased. This work has the potential to improve learning algorithms, increase understanding of neural memory formation, and inform neuromorphic engineering research. Full article

A natural phenomenon in applications is the interaction of quasi-periodic solutions of dynamical systems in a dissipative setting. We study the interactions of two of such ODE systems based on the construction of a nonlinear oscillator with thermostatic (energy) control. This leads to the emergence of complexity, torus doubling, and chaos. We find canards; 1-, 2-, and 3-tori; chaos, and hyperchaos. Detailed analysis is possible in the case of small oscillations and small interactions. Large-scale phenomena are studied by the construction of charts of parameter space using Lyapunov exponents. Full article

This research explores the dynamic characteristics of the soliton neuron model, a mathematical approach used to describe various complicated processes in neuroscience, including the unclear mechanisms of numerous anesthetics. An appropriate wave transformation converts the neuron model into a two-dimensional dynamical system, which takes the form of a conservative Hamiltonian system with a single degree of freedom. This study utilizes qualitative methods from planar integrable systems theory to analyze and interpret phase portraits. The conditions under which periodic, super-periodic, and solitary wave solutions exist are clearly defined and organized into theorems. These solutions are obtained analytically, with several examples depicted through 2D- and 3D-dimensional graphical illustrations. The research also examines how key physical parameters, such as frequency and sound velocity, affect the nature of these solutions, specifically on the width and the amplitude of those solutions. In addition, by inserting a generalized periodic external force, the model exhibits quasi-periodic and chaotic dynamics. These complicated dynamics are visualized using 2D and 3D phase portraits and time series plots. To further assess chaotic behavior, Lyapunov exponents are calculated. Numerical results indicate that the system’s overall behavior is strongly impacted by changes in the external force’s frequency and amplitude. Full article

A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin–Meshkov–Glick model under quasi-periodic Thue–Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host “quasi-discrete time crystal” (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of “all-to-all” interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems. Full article

MWC 342 (V1972 Cyg) was discovered nearly 90 years ago as an early-type emission-line star. It was among the first hot stars whose strong infrared excess was detected in the early 1970s. Several mostly short-term photometric and spectroscopic studies resulted in contradictory conclusions about the nature and evolutionary status of MWC 342. It has been classified as a pre-main-sequence Herbig Be star, an evolved suspected binary system, and a long-period variable star. Suggestions on the nature of the secondary component to this B0/B1 primary included a cool M-type giant and an X-ray source. We collected medium- and high-resolution optical spectra of MWC 342 taken in 1994–2024 as well as optical photometric data taken in 1986–2024. Analysis of these data shows strong variations in the object’s brightness and spectral line properties at various time scales, but no strictly periodic phenomena have been found. Inparticular, such a long-term dataset allowed us to reveal the optical brightness variations over a nearly 20-year-long quasi-period, as well as their anti-correlation with the H$\alpha$ emission-line strength. Also, we did not confirm the presence of He ii emission lines and absorption lines of the star’s atmosphere that were suspected in previously published studies. Full article

Lipid nanoparticles (LNPs) are widely recognized as effective drug delivery systems for RNA therapeutics because their efficacy is critically dependent on structural organization. The mesoscopic architecture of these multicomponent systems, which is governed by interactions among ionizable lipids, structural lipids, nucleic acids, and stabilizers, dictates encapsulation efficiency, biodistribution, and therapeutic performance. Although small-angle X-Ray scattering (SAXS) enables nanostructure characterization, the absence of suitable analytical models has hindered LNP development. Here, we present a core-triple shell SAXS model that resolves LNP hierarchical organization, including the inner lipid layer, intermediate hydrophilic region, and outer PEG corona. For LNPs encapsulating mRNA, a Gaussian distribution model was implemented to characterize the quasi-periodic structure originating from the self-assembly of mRNA-ionizable lipid complexes. Validation studies employing Comirnaty-based LNPs demonstrated that controlled variation of nitrogen-to-phosphorus (N/P) ratios produced distinguishable structural features that establish quantitative correlations between N/P ratios and LNP mesoscopic assembled structure. The modeling framework provides pharmaceutical researchers with robust analytical tools for systematic stability assessment and precision formulation for the optimization of LNPs. These structural insights are expected to advance the development of next-generation RNA therapeutics by potentially enhancing their delivery efficiency and pharmacokinetic properties. Full article

Magneto-electro-elastic materials, a novel class of smart materials, exhibit remarkable energy conversion properties, making them highly suitable for applications in nanotechnology. This study focuses on various aspects of the fractional nonlinear longitudinal wave equation (FNLWE) that models wave propagation in a magneto-electro-elastic circular rod. Using the direct algebraic method, several new soliton solutions were derived under specific parameter constraints. In addition, Galilean transformation was employed to explore the system’s sensitivity and quasi-periodic dynamics. The study incorporates 2D, 3D, and time-series visualizations as effective tools for analyzing quasi-periodic behavior. The results contribute to a deeper understanding of the nonlinear dynamical features of such systems and demonstrate the robustness of the applied methodologies. This research not only extends existing knowledge of nonlinear wave equations but also introduces a substantial number of new solutions with broad applicability. Full article

The Bronnikov generalization of the Fisher naked singularity and Dilatonic black hole spacetimes attracts high interest, as it combines two fundamental transitions of the solutions of Einstein equations. These are the black hole/wormhole “black bounce” transition of geometry, and the phantom/canonical transition of the scalar field, called trapped ghost scalar, combined with an electromagnetic field described by a non-linear electrodynamics. In the present paper, we put restrictions on the parameters of the Fisher (wormhole) and Dilatonic (black hole or wormhole) regularized spacetimes by using frequencies of the epicyclic orbital motion in the geodesic model for explanation of the high-frequency oscillations observed in microquasars or active galactic nuclei, where stellar mass or supermassive black holes are usually assumed. Full article

Low-energy ion bombardment (IB) has emerged as a promising, maskless nanofabrication tool for quasi-periodic nanoripples, marked by a high throughput and low cost. As templates, these IB-induced, self-organized surface nanoripples have shown potential for applications in diverse fields. However, the challenge of tailoring the ordering of these ripple patterns is preventing the widespread application of IB. Moreover, the enhancement of the ordering of these self-organized nanostructures involves the fundamental academic questions of nanoripple coupling (or superimposition) and guided self-organization. This review first focuses on the experimental progress made in developing representative strategies for the ordering enhancement of IB-induced nanoripples in terms of ion beams and targets. Second, we present our understanding of these developments from the perspectives of ripple superposition and guided self-organization. In particular, the basic conditions for ripple superposition under the non-conservation of mass are deduced based on the common features of the results from rocking bombardments of a single material and the bombardment of bilayer systems, providing insight into the mechanisms at play and deepening our understanding of these experimental observations. Finally, areas for future research are given, with the aim of improving ripple ordering from the viewpoints of ripple superimposition and guided self-organization. All this may re-stimulate interest in this field and will be of importance in advancing the academic research and practical applications of IB-induced nanopatterns. Full article