Search Results (790)

This study examines the contrast in the nonlinear dynamics of Thrinax radiata Lodd. ex Schult. & Schult. f. Seed germplasm explored by optical and electrical signals. By integrating chaotic attractors for the modulation of the optical and electrical measurements, the research ensures high sensitivity monitoring of seed germplasm dynamics. Reflectance measurements and electrical responses were analyzed across different laser pulse energies using Newton–Leipnik and Rössler chaotic attractors for signal characterization. The optical attractor captured laser-induced changes in reflectance, highlighting nonlinear thermal effects, while the electrical attractor, through a custom-designed circuit, revealed electromagnetic interactions within the seed. Results showed that increasing laser energy amplified voltage magnitudes in both systems, demonstrating their sensitivity to energy inputs and distinct energy-dependent chaotic patterns. Fractional calculus, specifically the Caputo fractional derivative, was applied for modeling temperature distribution within the seeds during irradiation. Simulations revealed heat transfer about 1 °C in central regions, closely correlating with observed changes in chaotic attractor morphology. This interdisciplinary approach emphasizes the unique strengths of each method: optical attractors effectively analyze photoinduced thermal effects, while electrical attractors offer complementary insights into bioelectrical properties. Together, these techniques provide a realistic framework for studying seed germplasm dynamics, advancing knowledge of their responses to external perturbations. The findings pave the way for future applications and highlight the potential of chaos theory for early detection of structural and bioelectrical changes induced by external energy inputs, thereby contributing to sample protection. Our results provide quantitative dynamical descriptors of laser-evoked seed responses that establish a tractable framework for future studies linking these metrics to physiological outcomes. Full article

Fractional-order chaotic systems have received increasing attention over the past few years due to their ability to effectively model memory and complexity in nonlinear dynamics. Nonetheless, most of the research conducted so far has been on constant-order formulations, which still have some limitations in terms of adaptability and reality. Thus, to evade these limitations, we present a recently designed four-dimensional hyperchaotic Chen system with variable-order fractional (VOF) derivatives in the Liouville–Caputo sense. In comparison with constant-order systems, the new system possesses excellent performance in numerous aspects. Firstly, with the use of variable-order derivatives, the system becomes more adaptive and flexible, allowing the chaotic dynamics of the system to evolve with changing fractional orders. Secondly, large-scale numerical simulations are conducted, where phase portrait orbits and time series for differences in VOF directly illustrate the effect of the order function on the system’s behavior. Thirdly, qualitative analysis is performed with the help of phase portraits, time series, and Lyapunov exponents to confirm the system’s hyperchaotic behavior and sensitivity to initial and control parameters. Finally, the model developed demonstrates a wide range of dynamic behaviors, which confirms the sufficient efficiency of VOF calculus for modeling complicated nonlinear processes. Numerous analyses indicate that this research not only shows meaningful findings but also provides thoughtful methodologies that might result in subsequent research on fractional-order chaotic systems. Full article

Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely simple model consisting of alternating one-dimensional walks along the two spatial coordinates in bidimensional closed domains (hard wall billiards). The chaotic or regular behavior induced by the boundary shape in the deterministic classical motion translates into chaotic signatures for the quantized problem, resulting in sharp differences in the spectral statistics and morphology of the eigenfunctions of the quantum walker. Indeed, we found, for the Bunimovich stadium—a chaotic billiard—level statistics described by a Brody distribution with parameter $\delta \simeq 0.1$. This indicates a weak level repulsion, and also enhanced eigenfunction localization, with an average participation ratio $(\mathrm{PR})\simeq 1150$ compared to the rectangular billiard (regular) case, where the average $\mathrm{PR}\simeq 1500$. Furthermore, scarring on unstable periodic orbits is observed. The fact that our simple model exhibits such key signatures of quantum chaos, e.g., non-Poissonian level statistics and scarring, that are sensitive to the underlying classical dynamics in the free particle billiard system is utterly surprising, especially when taking into account that quantum walks are diffusive models, which are not direct quantizations of a Hamiltonian. Full article

The power system’s dynamic frequency stability is affected by common-mode ultra-low-frequency oscillation and differential-mode low-frequency oscillation. Traditional frequency control based on generators is facing the problem of capacity reduction. It is urgent to explore new regulation resources such as photovoltaics. To address this issue, this paper proposes a distributed active support method based on photovoltaic systems via state–disturbance observation and dynamic surface consensus control. A three-layer distributed control framework is constructed to suppress low-frequency oscillations and ultra-low-frequency oscillations. To solve the high-order problem of the regional grid model and to obtain its unmeasurable variables, a regional observer estimating both system states and external disturbances is designed. Furthermore, a distributed dynamic frequency stability control method is proposed for wide-area photovoltaic clusters based on the dynamic surface control theory. In addition, the stability of the proposed distributed active support method has been proven. Moreover, a parameter tuning algorithm is proposed based on improved chaos game theory. Finally, simulation results demonstrate that, even under a 0–2.5 s time-varying communication delay, the proposed method can restrict the frequency deviation and the inter-area frequency difference index to 0.17 Hz and 0.014, respectively. Moreover, under weak communication conditions, the controller can also maintain dynamic frequency stability. Compared with centralized control and decentralized control, the proposed method reduces the frequency deviation by 26.1% and 17.1%, respectively, and shortens the settling time by 76.3% and 42.9%, respectively. The proposed method can effectively maintain dynamic frequency stability using photovoltaics, demonstrating excellent application potential in renewable-rich power systems. Full article

Fractional-order chaotic systems have emerged as powerful tools in secure communications and multimedia protection owing to their memory-dependent dynamics, large key spaces, and high sensitivity to initial conditions. However, most existing fractional-order image encryption schemes rely on fixed-order chaos and conventional solvers, which limit their complexity and reduce unpredictability, while also neglecting the potential of variable fractional-order (VFO) dynamics. Although similar phenomena have been reported in some fractional-order systems, the coexistence of hidden attractors and stable equilibria has not been extensively investigated within VFO frameworks. To address these gaps, this paper introduces a novel discrete variable fractional-order dark matter–dark energy (VFODM-DE) chaotic system. The system is discretized using the piecewise constant argument discretization (PWCAD) method, enabling chaos to emerge at significantly lower fractional orders than previously reported. A comprehensive dynamic analysis is performed, revealing rich behaviors such as multistability, symmetry properties, and hidden attractors coexisting with stable equilibria. Leveraging these enhanced chaotic features, a pseudorandom number generator (PRNG) is constructed from the VFODM-DE system and applied to grayscale image encryption through permutation–diffusion operations. Security evaluations demonstrate that the proposed scheme offers a substantially large key space (approximately $2^{249}$) and exceptional key sensitivity. The scheme generates ciphertexts with nearly uniform histograms, extremely low pixel correlation coefficients (less than 0.04), and high information entropy values (close to 8 bits). Moreover, it demonstrates strong resilience against differential attacks, achieving average NPCR and UACI values of about 99.6% and 33.46%, respectively, while maintaining robustness under data loss conditions. In addition, the proposed framework achieves a high encryption throughput, reaching an average speed of 647.56 Mbps. These results confirm that combining VFO dynamics with PWCAD enriches the chaotic complexity and provides a powerful framework for developing efficient and robust chaos-based image encryption algorithms. Full article

This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical system. Due to its non-Hamiltonian nature, this system poses significant analytical challenges. To overcome this complexity, the dynamical behavior is examined within a specific phase–space subspace, where the system simplifies to a two-dimensional, single-degree-of-freedom Hamiltonian system. The qualitative theory of planar dynamical systems is then employed to characterize the corresponding phase portraits. Bifurcation analysis identifies the physical parameter conditions that give rise to super-periodic, periodic, and solitary wave solutions. These solutions are derived analytically and illustrated graphically to highlight the influence of the fractional derivative order on their spatial and temporal evolution. Furthermore, when an external generalized periodic force is introduced, the model exhibits quasi-periodic behavior followed by chaotic dynamics. Both configurations are depicted through 3D and 2D phase portraits in addition to the time-series graphs. The presence of chaos is quantitatively verified by calculating the Lyapunov exponents. Numerical simulations demonstrate that the system’s behavior is highly sensitive to variations in the frequency and amplitude of the external force. Full article

Background: In the dynamic world of commercial aviation, the efficient management of ground handling (GH) operations in aircraft turnarounds is an increasingly complex challenge, often perceived as operational chaos. Methods: This paper introduces the “Critical Minute Theorem” (CMT), a novel framework that integrates mathematical architecture principles into the optimization of GH processes. CMT identifies singular temporal thresholds, $t_k^{\mathrm{*}}$ at which small local disturbances generate nonlinear, system-wide disruptions. Results: By formulating the turnaround as a set of algebraic dependencies and nonlinear differential relations, the case studies demonstrate that delays are not random but structurally determined. The practical contribution of this study lies in showing that early recognition and intervention at these critical minutes significantly reduces propagated delays. Three case analyses are presented: (i) a fueling delay initially causing 9 min of disruption, reduced to 3.7 min after applying CMT-based reordering; (ii) baggage mismatch scenarios where CMT-guided list restructuring eliminates systemic deadlock; and (iii) PRM assistance delays mitigated by up to 12–15 min through anticipatory task reorganization. Conclusions: These results highlight that CMT enables predictive, non-technological control in turnaround operations, repositioning the human analyst as an architect of time capable of restoring structure where the system tends to collapse. Full article

This paper investigates the nonlinear dynamics behavior and practical realization of a V/Heart-shape chaotic system. Nonlinear analysis contemporary tools, including bifurcation diagram, Lyapunov exponents, phase portraits, power spectral density (PSD) bicoherence, and spectral entropy (SE), are employed to investigate the system’s complex dynamical behaviors. To discover the system’s versatility, two case studies are presented by varying key system parameters, revealing various strange attractors. The system is modeled and implemented using an industrial-grade programmable logic controller (PLC) with structured text (ST) language, enabling robust hardware execution. The dynamics of the chaotic system are simulated, and the results are rigorously compared with experimental data from laboratory hardware implementations, demonstrating excellent agreement. The results indicate the potential usage of the proposed chaotic system for advanced industrial applications, secure communication, and dynamic system analysis. The findings confirm the successful realization of the V-shape and Heart-shape Chaotic Systems on PLC hardware, demonstrating consistent chaotic behavior across varying parameters. This practical implementation bridges the gap between theoretical chaos research and real-world industrial applications. Full article

This paper proposes a numerical technique to study dynamical systems and uncover new behaviors in chaotic fractional-order models, a field that continues to attract significant research interest due to its broad applicability and the ongoing development of innovative methods. Through various types of simulations, this approach is able to uncover novel dynamic behaviors that were previously undiscovered. The results guarantee that initial conditions and fractional-order derivatives have a significant contribution to system dynamics, thus distinguishing fractional systems from traditional integer-order models. The approach demonstrated has excellent consistency with traditional approaches for integer-order systems while offering higher accuracy for fractional orders. Consequently, this approach serves as a powerful and efficient tool for studying complex chaotic models. Fractional-order dynamical systems (FDSs) are particularly noteworthy for their ability to model memory and hereditary characteristics. The method identifies new complex phenomena, including new chaos, unusual attractors, and complex time-series patterns, not documented in the existing literature. We use Lyapunov exponents, bifurcation analysis, and Poincaré sections to thoroughly investigate the system dynamics, with particular emphasis on the effect of fractional-order and initial conditions. Compared to traditional integer-order approaches, our approach is more accurate and gives a more efficient device for facilitating research on fractional-order chaos. Full article

The sustainability of Korla fragrant pear orchards has been increasingly threatened by prolonged intensive agricultural practices. In response, biofertilizers and green manures have gained attention due to their potential to enhance soil structure, activate microbial functions, and improve nutrient uptake. However, the dynamic changes in soil bacterial communities under such interventions remain inadequately understood. This study was conducted from 2022 to 2023 in 7- to 8-year-old Korla fragrant pear orchards in Bayin’guoleng Mongol Autonomous Prefecture, Xinjiang. The treatments included: conventional fertilization (CK), biofertilizer (JF), oil sunflowers (DK1) with 25 cm row spacing and a seeding rate of 27 kg·hm⁻², oil sunflowers (DK2) with 25 cm row spacing and a seeding rate of 33 kg·hm⁻², sweet clover (CM1) with 20 cm row spacing and a seeding rate of 21 kg·hm⁻², and sweet clover (CM2) with 20 cm row spacing and a seeding rate of 27 kg·hm⁻². During the 2023 pear season, soil samples from the 0–20 cm layer were collected at the fruit setting, expansion, and maturity stages. Their physical and chemical properties were analyzed, and the structure and diversity of the soil bacterial community were examined using 16S rRNA gene high-throughput sequencing. Fruit yield was assessed at the maturity stage. Compared to CK, the relative abundance of Actinobacteria increased by 101.00%, 38.99%, and 50.38% in the JF, DK2, and CM1 treatments, respectively. DK1 and CM1 treatments resulted in a 152.28% and 145.70% increase in the relative abundance of the taxon Subgroup_7, while JF and DK2 treatments enhanced the relative abundance of the taxon Gitt-GS-136 by 318.91% and 324.04%, respectively. The Chao1 index for CM2 was 18.76% higher than CK. LEfSe analysis showed that the DK2 and CM2 treatments had a more significant regulatory effect on bacterial community structure. All treatments led to higher fruit numbers and yield compared to CK, with JF showing the largest yield increase. Fertilizer type, soil nutrients, and bacterial community structure all significantly positively influenced pear yield. In conclusion, high-density oil sunflower planting is the most effective approach for maintaining soil microbial community stability, followed by low-density sweet clover. This study provides a systematic evaluation of the dynamic effects of bio-fertilizers and different green manure planting patterns on soil microbial communities in Korla fragrant pear orchards, presenting practical, microbe-based strategies for sustainable orchard management. Full article

Urban flooding represents a growing concern on a global scale, particularly in regions characterized by rapid urbanization and increased climate variability. This study concentrates on the Rangsit area in Pathum Thani Province, Thailand, an urbanizing peri-urban area north of Bangkok and within the Chao Phraya River Basin where transitions in land use and the intensification of rainfall induced by climate change are elevating flood risks. A physically based hydrodynamic model was developed utilizing PCSWMM to assess current and future flood scenarios that considered future build-out plans and climate change scenarios. The model underwent calibration and validation using a continuous modeling approach that conservatively focused on wet year conditions, based on available rainfall and water level data. In assessing future scenarios, we considered land use projections based on regional development plans and climate projections downscaled under RCP4.5 and RCP8.5 pathways. Results indicate that both urban expansion and intensifying rainfall are likely to increase flood magnitudes, durations, and impacted areas, although in this rapidly developing peri-urban area, land use change was the most important driver. The findings suggest that a physically based modeling approach could support a smart-control framework that could effectively inform evidence-based urban planning and infrastructure investments. These insights are of paramount importance for flood-prone regions in Thailand and Southeast Asia, where dynamic modeling tools must underpin governance, climate adaptation, and risk communication. Furthermore, given the greater impact of future build-out on flood risk, as compared to climate change, there is an opportunity to effectively and proactively improve flood resilience through the implementation of integrated Nature-based Solution and hard engineering approaches, in combination with effective flood management policy. Full article

Kolmogorov–Sinai (KS) entropy is an indicator of the chaotic behavior of entire systems from an information-theoretic viewpoint. Here, we used KS entropy values derived from the heart sounds of four fetus–mother pairs to identify the changes in fetal and maternal informational patterns during the four phases of pregnancy (early, mid, late, and postnatal). Time-series data of the heart sounds were reconstructed in a five-dimensional phase space to obtain the Lyapunov spectrum, and KS entropy was calculated. Statistical analyses were then conducted separately for the fetus and mother for the four phases of pregnancy. The fetal KS entropy significantly increased from early pregnancy to the postnatal period (0.054 ± 0.007 vs. 0.097 ± 0.007; p < 0.001), whereas the maternal KS entropy decreased in late pregnancy and then significantly increased after birth (0.098 ± 0.002 vs. 0.133 ± 0.003; p < 0.001). The increase in KS entropy with the course of fetal gestation reflects an increase in information generation and adaptive capacity during the developmental process. Thus, changes in maternal KS entropy play a dual role, temporarily enhancing physiological stability to support fetal development and helping to rebuild the mother’s own adaptive capacity in the postpartum period. Full article

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article

This study explores the nonlinear dynamics and interdependencies among major commodity markets—Gold, Oil, Natural Gas, and Silver—by employing advanced chaos theory and information-theoretic tools. Using daily data from 2020 to 2024, we estimate key complexity measures including Lyapunov exponents, correlation dimension, Shannon and Rényi entropy, and mutual information. We also apply the stochastic SO(2) Lie group method to model dynamic correlations, and wavelet coherence analysis to detect time-frequency co-movements. Our findings reveal evidence of low-dimensional deterministic chaos and time-varying nonlinear relationships, especially among pairs like Gold–Silver and Oil–Gas. These results highlight the importance of using nontraditional approaches to uncover hidden structure and co-movement dynamics in commodity markets, providing useful insights for portfolio diversification and systemic risk assessment. Full article

In this study, the complete discrimination system for the polynomial method (CDSPM) is employed to analyze the integrable Gardner Equation (IGE). Through a traveling wave transformation, the model is reduced to a nonlinear ordinary differential equation, enabling the derivation of a wide class of exact solutions, including trigonometric, hyperbolic, rational, and Jacobi elliptic functions. For example, a bright soliton solution is obtained for parameters $A=1.3$, $\beta =-0.1$, and $\gamma =0.8$. Qualitative analysis reveals diverse phase portraits, indicating the presence of saddle points, centers, and cuspidal points depending on parameter values. Chaos and quasi-periodic dynamics are investigated via Poincaré maps and time-series analysis, where chaotic patterns emerge for values like ${\nu }_1=1.45$, ${\nu }_2=2.18$, ${\Xi }_0=4$, and $\lambda =2\pi$. Sensitivity analysis confirms the model’s sensitivity to initial conditions $\chi =2.2,2.4,2.6$, reflecting real-world unpredictability. Additionally, the energy balance method (EBM) is applied to approximate periodic solutions by conserving kinetic and potential energies. These results highlight the IGE’s ability to capture complex nonlinear behaviors relevant to fluid dynamics, plasma waves, and nonlinear optics. Full article