Search Results (78)

Background/Objectives: Poincaré plot analysis represents a nonlinear approach to heart rate variability (HRV) assessment, but the physiological meaning of several derived parameters remains unclear. This study aimed to evaluate associations between selected Poincaré plot-derived parameters, conventional HRV indices, and cardiovascular autonomic reflex tests in a real-world clinical population. Methods: This observational study included 269 adult patients referred for evaluation of suspected autonomic dysfunction. All participants underwent short-term resting ECG, cardiovascular autonomic reflex testing, and 24 h Holter ECG monitoring. Poincaré plot-derived parameters were analyzed in relation to short- and long-term HRV measures using the Spearman correlation with false discovery rate correction, and group comparisons were performed based on reflex test results. Results: Several Poincaré plot-derived parameters showed strong correlations with long-term HRV indices. VLI and LA were primarily associated with global and long-term autonomic variability, whereas VAI and SA were more closely related to parasympathetic modulation. Associations with short-term HRV were generally weak. Lower values of selected parameters were observed in patients with abnormal parasympathetic reflex tests, while no significant differences were found in relation to orthostatic hypotension. Conclusions: Poincaré plot-derived parameters capture complementary aspects of autonomic regulation beyond conventional HRV indices and may enhance autonomic phenotyping in clinical settings. Full article

In this paper, we investigate the (1 + 1)-dimensional nonlinear truncated M-fractional FitzHugh–Nagumo model. The main objective is to analyze the dynamical behavior and obtain exact solutions for the model. First, a fractional transformation is applied to convert the governing partial differential equation into an ordinary differential equation. Subsequently, a Galilean transformation is employed to reduce the resulting equation to a dynamical system. The bifurcation structure and chaotic dynamics of the model are then examined. The presence of chaos is further confirmed through the phase portrait, basin of attraction, return map, Lyapunov exponent, permutation entropy, Poincaré map, power spectrum, attractor, fractal dimension, multistability, time analysis, and recurrence plot. In addition, the sensitivity of the system to the initial conditions is analyzed. Finally, exact solutions for the model are constructed using the unified Riccati equation expansion method. The obtained results are illustrated using two-dimensional, three-dimensional, and contour plots. Full article

Background/Objectives: Aortic stenosis is associated with autonomic nervous system (ANS) imbalance, while diabetes mellitus is a major contributor to cardiac autonomic neuropathy. Their coexistence may result in more pronounced autonomic dysfunction not fully captured by conventional assessment. This study aimed to compare ANS function in patients with severe aortic stenosis undergoing transcatheter aortic valve replacement (TAVR), according to diabetes status. Methods: This cross-sectional study included 74 patients with severe aortic stenosis referred for TAVR, including 21 patients with diabetes mellitus. Autonomic function was evaluated using non-invasive ECG-based analysis, incorporating short-term and 24 h Holter-derived heart rate variability (HRV), nonlinear Poincaré plot indices, and deceleration and acceleration capacity. Ambulatory blood pressure monitoring and standard clinical and echocardiographic assessment were performed. Results: Patients with diabetes mellitus demonstrated significantly lower long-term HRV parameters and reduced nonlinear Poincaré plot indices compared with non-diabetic patients, indicating altered autonomic modulation. Short-term HRV showed similar trends without statistical significance. Echocardiographic severity of aortic stenosis and left ventricular systolic function were comparable between groups. Conclusions: Autonomic dysfunction appears to be more pronounced in patients with severe aortic stenosis and diabetes mellitus, predominantly affecting parasympathetic modulation. ECG-derived autonomic parameters may offer complementary insight into ANS involvement in this population and warrant further investigation. Full article

The development of portable electrocardiographic analysis systems necessitates identifying an optimal balance between diagnostic precision and computational efficiency. This research addresses the challenge of optimal feature selection for automated cardiac arrhythmia classification in resource-constrained portable applications. We present a comparative investigation of three distinct feature selection strategies for ECG classification: the MRMR (Minimum Redundancy Maximum Relevance) method, which maximizes relevance while minimizing feature interdependencies; the ReliefF technique, which evaluates discriminative power through proximity analysis in the feature space; and permutation-based importance analysis implemented with neural networks. Utilizing the Large-Scale 12-Lead Electrocardiogram Database for Arrhythmia Study, we construct a hybrid feature space integrating 12 conventional time- and frequency-domain parameters (previously validated and included in the database’s official documentation) with 26 advanced nonlinear descriptors, including the Hurst exponent, DFA scaling parameter, log-absolute correlation measures, mean standard increment from the Poincaré plot, and wavelet entropy. The experimental results demonstrate remarkable convergence among the three paradigms in selecting optimal feature subsets, achieving classification accuracies of 87–89% for four arrhythmia classes using compact configurations of 7–10 features, and 93.57% with an extended 12-parameter set. The 7-feature configuration achieves an 82% complexity reduction compared to the full 38-feature set. Multi-algorithmic analysis confirms the consistent discriminative contribution of the proposed nonlinear descriptors, demonstrating that MRMR, ReliefF, and permutation analyses yield convergent rankings of critical parameters for automated cardiac pathology diagnosis. Full article

Stochastically forced nonlinear wave systems are commonly associated with complex dynamical behavior, although little is known about the general interaction of nonlinear dispersion, irrational forcing frequencies, and multiplicative noise. To fill this gap, we consider a generalized stochastic SIdV equation and examine the effects of deterministic and stochastic influences on the long-term behavior of the equation. The PDE was modeled using a stochastic traveling-wave transformation that simplifies it into a planar system, which was studied using Darboux-seeded constructions, Poincaré maps, bifurcation patterns, Lyapunov exponents, recurrence plots, and sensitivity diagnostics. We discovered that natural, implicit, and unique seeds produce highly diverse transformed wave fields exhibiting both irrational and golden-ratio forcing, controlling the transition from quasi-periodicity to chaos. Stochastic perturbation is demonstrated to suppress as well as to amplify chaotic states, based on noise levels, altering attractor geometry, predictability, and multistability. Meanwhile, OGY control is demonstrated to be able to stabilize chosen unstable periodic orbits of the double-well regime. A stochastic bifurcation analysis was performed with respect to noise strength $\sigma$, revealing that the attractor structure of the system remains robust under stochastic excitation, with noise inducing only bounded fluctuations rather than qualitative dynamical transitions within the investigated parameter regime. These findings demonstrate that the emergence, deformation, and controllability of complex oscillatory patterns of stochastic nonlinear wave models are jointly controlled by nonlinear structure, external forcing, and noise. Full article

Objective: The aim of this study was to analyse the evolution of heart rate variability (HRV) during official competition in high-level amateur padel players according to match outcome. Methods: HRV was measured in 44 individual recordings obtained across 11 matches involving 12 padel players. Measurements were taken before the match (PRE), during three sets (S1, S2 and S3) and during the two rest periods between sets (R1 and R2). Time-domain variables analysed included mean R–R interval (Mean RR), standard deviation of normalised R–R intervals (SDNN), root mean square of successive differences (RMSSD), natural logarithm of RMSSD (LnRMSSD) and standard deviation of heart rate (STD HR), while nonlinear variables included the transverse (SD1) and longitudinal (SD2) axes of the Poincare plot, stress score (SS) and the sympathetic–parasympathetic ratio (SNS/PNS ratio). Results: Significant fluctuations in HRV were observed throughout the match. Players who won exhibited significantly higher values of Mean RR, SDNN, RMSSD, LnRMSSD, SD1 and SD2 during S1 (p < 0.05), and higher Mean RR, RMSSD, LnRMSSD and SD1 during R1 (p < 0.01). These differences diminished as the match progressed, disappearing in the later phases (S3, R2). Temporal analysis revealed that both groups showed parasympathetic recovery during the rest periods. Conclusions: This study provides novel evidence on the temporal dynamics of autonomic regulation in padel, showing that match outcome is associated with differences in cardiovascular regulation during the initial phases of competition. These findings support the usefulness of HRV monitoring for performance management in real competition settings. Full article

The (3 + 1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation, a model that describes long-wave interactions and has numerous applications in mathematics, engineering, and physics, is examined in this work. First, a wave transformation is used to reduce the equation to lower dimensions. The modified Khater method is then used to derive different types of solitary wave solutions, such as chirped, kink, periodic, and kink-bright types. By allocating suitable constant parameters, 3D, 2D, and contour plots are created to demonstrate the physical behavior of these solutions. Phase portraits are used to qualitatively analyze the undisturbed planar system using bifurcation theory. The system is then perturbed by an external force, resulting in chaotic dynamics. Chaos in the system is confirmed using multiple diagnostic tools, including time series plots, Poincaré sections, chaotic attractors, return maps, bifurcation diagrams, power spectra, and Lyapunov exponents. The stability of the model is further investigated with varying initial conditions. A bidirectional scatter plot technique, which efficiently reveals overlapping regions using data point distributions, is presented for comparing solution behaviors. Overall, this work offers useful tools for advancing applied mathematics research as well as a deeper understanding of nonlinear wave dynamics. 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 paper presents a comprehensive dynamical analysis of a nonlinear oscillator subjected to both deterministic and stochastic excitations. Utilizing a diverse suite of analytical tools—including phase portraits, Poincaré sections, Lyapunov exponents, recurrence plots, Fokker–Planck equations, and sensitivity diagnostics—we investigate the transitions between quasi-periodicity, chaos, and stochastic disorder. The study reveals that quasi-periodic attractors exhibit robust topological structure under moderate noise but progressively disintegrate as stochastic intensity increases, leading to high-dimensional chaotic-like behavior. Recurrence quantification and Lyapunov spectra validate the transition from coherent dynamics to noise-dominated regimes. Poincaré maps and sensitivity analysis expose multistability and intricate basin geometries, while the Fokker–Planck formalism uncovers non-equilibrium steady states characterized by circulating probability currents. Together, these results provide a unified framework for understanding the geometry, statistics, and stability of noisy nonlinear systems. The findings have broad implications for systems ranging from mechanical oscillators to biological rhythms and offer a roadmap for future investigations into fractional dynamics, topological analysis, and data-driven modeling. Full article

The Poincaré plot was introduced as a tool to analyze heart rate variations caused by arrhythmias. Later, it was applied to time series with normal beats. The plot shows the relationship between the inter-beat interval (IBI) of one beat to the next. Several parameters were developed to characterize this relationship. The short and long axis of the fitting ellipse, SD1 and SD2, respectively, their ratio, and their product are used. The difference between the IBI of a beat and m beats later are also studied, SD1(m) and SD2(m). We studied the mathematical relations between heart rate variability measures and the Poincaré measures in the time (standard deviation of IBI, SDNN, root mean square of successive differences, RMSSD) and frequency domain (power in low and high frequency band, and their ratio). We concluded that SD1 and SD2 do not provide new information compared to SDNN and RMSSD. Only the correlation coefficient r(m) provides new information for m > 1. Novel findings are that ln(SD2(m)/SD1(m)) = tanh⁻¹(r(m)), which is an approximately normal distributed transformation of r(m), and that SD1(m) and SD2(m) can be calculated by multiplying the power spectrum by a weighing function that depends on m, revealing the relationship with spectral measures, but also the relationship between SD1(m) and SD2(m). Both lagged parameters are extremely difficult to interpret compared to low and high frequency power, which are more closely related to the functioning of the autonomic nervous system. Full article

Background: Monitoring autonomic balance provides valuable insights into recovery status and physiological readiness, both of which are essential for performance optimization in athletes. The Stress Score (SS) and Sympathetic–Parasympathetic Ratio (SPS), derived from Poincaré plot heart rate variability (HRV) indices, have been proposed as practical markers of sympathetic activity and overall autonomic balance. However, these traditional calculations often require lengthy recordings and specialized software, limiting their feasibility in field settings. This study introduces modified versions of these metrics derived from ultra-short-term (1 min) time–domain HRV recordings: the Modified Stress Score (MSS) and Modified Sympathetic–Parasympathetic Ratio (MSPS). Methods: Competitive male athletes (n = 20, age = 21.2 ± 2.1 year, height = 183.6 ± 8.9 cm, weight = 79.2 ± 10.3 kg) completed a maximal exercise test with HRV recorded before and after exercise. Results: Following natural log-transformation, MSS and MSPS demonstrated strong correlations with SS and SPS across all time points (r = 0.87–0.94, all p < 0.01) and displayed the expected physiological responses to exercise and recovery. Conclusions: These findings suggest that MSS and MSPS are practical, accessible tools for assessing autonomic balance in athletes. Their application may enhance our ability to monitor recovery status, guide individualized training strategies, and optimize performance in applied sport settings. Full article

In the study of dynamic systems, bifurcation diagrams are a very popular graphical tool for studying stability and nonlinear changes in behavior. They are instrumental in analyzing the system’s response to parameter changes. These diagrams show the system’s various dynamic patterns and phase transitions by plotting the relationship between the system response and the parameters. This paper presents a computational algorithm for studying bifurcations in dynamic systems, especially for systems with chaotic behavior that depends on parameter changes. Depending on the type of system to be analyzed, the following two strategies for computing bifurcation diagrams are described: (i) detecting crossing points through the Poincaré plane and (ii) the identification of local maxima (or minima) in one of the system solutions. In addition, this paper presents a method for implementing parallel computation in MATLAB using the Parallel Computing Toolbox from MathWorks, which significantly reduces the computational time required to generate bifurcation diagrams. This work contributes to the study of dynamic systems by providing the reader with accessible tools for studying any dynamic system under established standards and reducing the computational time required for these types of studies by implementing these algorithms utilizing the multi-core processors found in modern computers. Full article

This article investigates the qualitative analysis and traveling wave solutions of a (3 + 1)-dimensional generalized nonlinear Konopelchenko-Dubrovsky-Kaup-Kupershmidt system. This equation is commonly used to simulate nonlinear wave problems in the fields of fluid mechanics, plasma physics, and nonlinear optics, as well as to transform nonlinear partial differential equations into nonlinear ordinary differential equations through wave transformations. Based on the analysis of planar dynamical systems, a nonlinear ordinary differential equation is transformed into a two-dimensional dynamical system, and the qualitative behavior of the two-dimensional dynamical system and its periodic disturbance system is studied. A two-dimensional phase portrait, three-dimensional phase portrait, sensitivity analysis diagrams, Poincaré section diagrams, and Lyapunov exponent diagrams are provided to illustrate the dynamic behavior of two-dimensional dynamical systems with disturbances. The traveling wave solution of a Konopelchenko-Dubrovsky-Kaup-Kupershmidt system is studied based on the complete discriminant system method, and its three-dimensional, two-dimensional graphs and contour plots are plotted. These works can provide a deeper understanding of the dynamic behavior of Konopelchenko-Dubrovsky-Kaup-Kupershmidt systems and the propagation process of waves. Full article

Background: Chronic pain has been reported as one of the leading causes of disability in the world, being associated with a potential impact on autonomic balance. Objective: The aim was to compare sympathetic and parasympathetic activity through heart rate variability (HRV) between adults with and without chronic low back pain (CLBP). Methods: An observational study was conducted in which HRV parameters were recorded using time-domain measures—root mean square of successive differences between consecutive RR intervals (rMSSD), minimum and maximum heart rate variability (Min HR and Max HR), and mean heart rate (Mean HR)—and nonlinear measures—Poincaré plot indices SD1 and SD2, Stress Score (SS), and sympathetic/parasympathetic ratio (S:PS). Results: The results showed statistically significant differences between groups (p < 0.05), with higher parasympathetic activity parameters in the group of healthy subjects (rMSSD: p < 0.001; SD1: p = 0.030) and higher sympathetic activity in the CLBP group (SD2, SS, and S:PS ratio: p < 0.001). All parameters showed large effect sizes. Conclusions: These findings show the association between autonomic balance mechanisms and pain regulation in adults with CLBP. Full article

We examined data from Naval Sea Systems Command grant project N0463A-12-C-001, “Hypercapnia: cognitive effects and monitoring”, with the objective of validating or repudiating heart rate variability (HRV) as a warning sign of cognitive impairment from diving gas narcosis or oxygen toxicity. We compared HRV feature scores to their temporally corresponding cognitive outcomes under normal and narcotizing conditions to identify specific HRV features associated with cognitive changes. N0463A-12-C-001 was conducted between 17 September 2013 and 29 January 2016 and employed NASA’s multi-attribute task battery (MATB-II) flight simulator to examine the independent effects of CO₂, N₂, and O₂ partial pressure on diver performance at simulated depths up to 61 msw (200 fsw). We assessed the association of 23 distinct HRV features scores from 432 of the study’s analyzable exposure stages in relation to MATB-II’s four performance subclasses (motor, memory, attention, strategy) while controlling for exercise and CO₂, N₂, and O₂ gas partial pressure. Performance decrements were associated with normalized high-frequency HRVfeatures (HFnu, p = 0.0016) and the number of pairs of successive R-R intervals that differed by more than 50 ms (NN50count1, p = 0.04). Secondary analysis with stratification restricted to non-exercise stages showed that several HRV parameters, including root mean square of the successive difference (RMSSD, p = 0.0015), width of Poincaré plot (p = 0.0017), NN50count1 (p = 0.0019), and standard deviation of normal-to-normal R peaks (p = 0.0082), were associated with performance impairment. The RMSSD association retained statistical significance after Bonferroni correction for multiple tests. HRV features collected from divers tested under narcotizing conditions of breathing gas partial pressure and exercise were associated with performance impairment. Full article