The theory of nonlinear dynamics was introduced to voice science in the 1990s and revolutionized our understanding of human voice production mechanisms. This theory elegantly explains highly complex phenomena in the human voice, such as subharmonic and rough-sounding voice, register breaks, and intermittent aphonic breaks. These phenomena occur not only in pathologic, dysphonic voices but are also explored for artistic purposes, such as contemporary singing. The theory reveals that sudden changes in vocal fold vibratory patterns and fundamental frequency can result from subtle alterations in vocal fold geometry, mechanical properties, adduction, symmetry or lung pressure. Furthermore, these changes can be influenced by interactions with supraglottal tract and subglottal tract resonances. Crucially, the eigenmodes (modes of vibration) of the vocal folds play a significant role in these phenomena. Understanding how the left and right vocal fold eigenmodes interact and entrain with each other, as well as their interplay with supraglottal tissues, glottal airflow and acoustic resonances, is essential for more sophisticated diagnosis and targeted treatment of voice disorders in the future. Additionally, this knowledge can be helpful in modern vocal pedagogy. This article reviews the concepts of nonlinear dynamics that are important for understanding normal and pathologic voice production in humans.This article is part of the theme issue 'Nonlinear phenomena in vertebrate vocalizations: mechanisms and communicative functions'.
- Klíčová slova
- dysphonia, entrainment, nonlinear phenomena, singing, vocal fold eigenmodes, voice production,
- MeSH
- hlas * fyziologie MeSH
- hlasové řasy * fyziologie MeSH
- lidé MeSH
- nelineární dynamika * MeSH
- poruchy hlasu * patofyziologie MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- přehledy MeSH
Voice is a major means of communication for humans, non-human mammals and many other vertebrates like birds and anurans. The physical and physiological principles of voice production are described by two theories: the MyoElastic-AeroDynamic (MEAD) theory and the Source-Filter Theory (SFT). While MEAD employs a multiphysics approach to understand the motor control and dynamics of self-sustained vibration of vocal folds or analogous tissues, SFT predominantly uses acoustics to understand spectral changes of the source via linear propagation through the vocal tract. Because the two theories focus on different aspects of voice production, they are often applied distinctly in specific areas of science and engineering. Here, we argue that the MEAD and the SFT are linked integral aspects of a holistic theory of voice production, describing a dynamically coupled system. The aim of this manuscript is to provide a comprehensive review of both the MEAD and the source-filter theory with its nonlinear extension, the latter of which suggests a number of conceptual similarities to sound production in brass instruments. We discuss the application of both theories to voice production of humans as well as of animals. An appraisal of voice production in the light of non-linear dynamics supports the notion that it can be best described with a systems view, considering coupled systems rather than isolated contributions of individual sub-systems.
- Klíčová slova
- MEAD, Myoelastic-aerodynamic theory, Phonation, Source-filter coupling, Source-filter interactions, Source-filter theory, Voice,
- MeSH
- akustika řeči * MeSH
- akustika MeSH
- biologické modely MeSH
- biomechanika MeSH
- fonace * MeSH
- hlasové řasy * fyziologie MeSH
- kvalita hlasu * MeSH
- lidé MeSH
- nelineární dynamika MeSH
- pružnost MeSH
- vibrace MeSH
- vokalizace zvířat MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- přehledy MeSH
Fractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions. For this reason, methods for approximating solutions that occasionally yield closed-form solutions are crucial for solving these equations. This study introduces a novel technique that combines the residual function and a modified fractional power series with the Elzaki transform to solve various nonlinear problems within the Caputo derivative framework. The accuracy and effectiveness of our approach are validated through analyses of absolute, relative, and residual errors. We utilize the limit principle at zero to identify the coefficients of the series solution terms, while other methods, including variational iteration, homotopy perturbation, and Adomian, depend on integration. In contrast, the residual power series method uses differentiation, and both approaches encounter difficulties in fractional contexts. Furthermore, the effectiveness of our approach in addressing nonlinear problems without relying on Adomian and He polynomials enhances its superiority over various approximate series solution techniques.
- MeSH
- algoritmy * MeSH
- nelineární dynamika * MeSH
- teoretické modely MeSH
- Publikační typ
- časopisecké články MeSH
This study explores the Ivancevic Option Pricing Model, a nonlinear wave-based alternative to the Black-Scholes model, using adaptive nonlinear Schrödingerr equations to describe the option-pricing wave function influenced by stock price and time. Our focus is on a comprehensive analysis of this equation from multiple perspectives, including the study of soliton dynamics, chaotic patterns, wave structures, Poincaré maps, bifurcation diagrams, multistability, Lyapunov exponents, and an in-depth evaluation of the model's sensitivity. To begin, a wave transformation is applied to convert the partial differential equation into an ordinary differential equation, from which soliton solutions are derived using the [Formula: see text] method. We explore various forms of the option price function at different time points, including singular-kink, periodic, hyperbolic, trigonometric, exponential, and complex solutions. Furthermore, we simulate 3D surface plots and 2D graphs for the real, imaginary, and modulus components of some of the obtained solutions, assigning specific parameter values to enhance visualization. These graphical representations offer valuable insights into the dynamics and patterns of the solutions, providing a clearer understanding of the model's behavior and potential applications. Additionally, we analyze the system's dynamic behavior when a perturbing force is introduced, identifying chaotic patterns using the Lyapunov exponent, Sensitivity, multistability analysis, RK4 method, wave structures, bifurcation diagrams, and Poincaré maps.
- MeSH
- algoritmy MeSH
- ekonomické modely * MeSH
- lidé MeSH
- náklady a analýza nákladů MeSH
- nelineární dynamika * MeSH
- obchod ekonomika MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
This article aims to study the time fractional coupled nonlinear Schrödinger equation, which explains the interaction between modes in nonlinear optics and Bose-Einstein condensation. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include novel solutions like a combined dark-lump wave soliton, multiple dark-lump wave soliton, two dark-kink solitons, flat kink-lump wave, multiple U-shaped with lump wave, combined bright-dark with high amplitude lump wave, bright-dark with lump wave and kink dark-periodic solitons are derived. The travelling wave patterns of the model are graphically presented with suitable parameters in 3D, density, contour and 2D surfaces, enhancing understanding of parameter impact. The proposed model's dynamics were observed and presented as quasi-periodic chaotic, periodic systems and quasi-periodic. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.
- MeSH
- algoritmy MeSH
- nelineární dynamika * MeSH
- teoretické modely MeSH
- Publikační typ
- časopisecké články MeSH
This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota's bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a number of three-wave solutions are derived. Applying the Lie symmetry approach to the governing equation enables the determination of symmetry reduction, which aids in the reduction of the dimensionality of the said equation. Using symmetry reduction, we obtain the second order differential equation. By means of applying symmetry reduction, the second order differential equation is derived. The second order differential equation undergoes Galilean transformation to obtain a system of first order differential equations. The present study presents an analysis of bifurcation and sensitivity for a given dynamical system. Additionally, when an external force impacts the underlying dynamic system, its behavior resembles quasi-periodic phenomena. The presence of quasi-periodic patterns are identified using chaos detecting tools. These findings represent a novel contribution to the studied equation and significantly advance our understanding of dynamics in nonlinear wave models.
- MeSH
- algoritmy MeSH
- nelineární dynamika * MeSH
- teoretické modely MeSH
- Publikační typ
- časopisecké články MeSH
OBJECTIVE: Dynamic systems theory and complexity theory (DST/CT) is a framework explaining how complex systems change and adapt over time. In psychotherapy, DST/CT can be used to understand how a person's mental and emotional state changes during therapy incorporating higher levels of complexity. This study aimed to systematically review the variability of DST/CT methods applied in psychotherapy research. METHODS: A primary studies search was conducted in the EBSCO and Web of Knowledge databases, extracting information about the analyzed DST/CT phenomena, employed mathematical methods to investigate these phenomena, descriptions of specified dynamic models, psychotherapy phenomena, and other information regarding studies with empirical data (e.g., measurement granularity). RESULTS: After screening 38,216 abstracts and 4,194 full texts, N = 41 studies published from 1990 to 2021 were identified. The employed methods typically included measures of dynamic complexity or chaoticity. Computational and simulation studies most often employed first-order ordinary differential equations and typically focused on describing the time evolution of client-therapist dyadic influences. Eligible studies with empirical data were usually based on case studies and focused on data with high time intensity of within-session dynamics. CONCLUSION: This review provides a descriptive synthesis of the current state of the proliferation of DST/CT methods in the psychotherapy research field.
- Klíčová slova
- chaos theory, complex systems, differential equations, nonlinearity, psychotherapy, systematic review,
- MeSH
- adaptace psychologická MeSH
- lidé MeSH
- nelineární dynamika * MeSH
- psychologie * metody MeSH
- psychoterapie * MeSH
- systémová teorie * MeSH
- teoretické modely MeSH
- vizualizace dat MeSH
- výzkumný projekt * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- systematický přehled MeSH
Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons' propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.
Applications of causal techniques to neural time series have increased extensively over last decades, including a wide and diverse family of methods focusing on electroencephalogram (EEG) analysis. Besides connectivity inferred in defined frequency bands, there is a growing interest in the analysis of cross-frequency interactions, in particular phase and amplitude coupling and directionality. Some studies show contradicting results of coupling directionality from high frequency to low frequency signal components, in spite of generally considered modulation of a high-frequency amplitude by a low-frequency phase. We have compared two widely used methods to estimate the directionality in cross frequency coupling: conditional mutual information (CMI) and phase slope index (PSI). The latter, applied to infer cross-frequency phase-amplitude directionality from animal intracranial recordings, gives opposite results when comparing to CMI. Both metrics were tested in a numerically simulated example of unidirectionally coupled Rössler systems, which helped to find the explanation of the contradictory results: PSI correctly estimates the lead/lag relationship which, however, is not generally equivalent to causality in the sense of directionality of coupling in nonlinear systems, correctly inferred by using CMI with surrogate data testing.
- Klíčová slova
- Conditional mutual information, Coupling directionality, Cross-frequency coupling, EEG, Nonlinear systems, Phase slope index,
- MeSH
- elektroencefalografie * metody MeSH
- lidé MeSH
- modely neurologické MeSH
- mozek fyziologie MeSH
- nelineární dynamika * MeSH
- počítačová simulace MeSH
- počítačové zpracování signálu MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- srovnávací studie MeSH
The basilar membrane in the cochlea can be modeled as an array of fluid coupled segments driven by stapes vibration and by the undamping nonlinear force simulating cochlear amplification. If stimulated with two tones, the model generates additional tones due to nonlinear distortion. These distortion products (DPs) can be transmitted into the ear canal and produce distortion-product otoacoustic emissions (DPOAEs) known to be generated in the healthy ear of various vertebrates. This study presents a solution for DPs in a two-dimensional nonlinear cochlear model with cochlear roughness-small irregularities in the impedance along the basilar membrane, which may produce additional DPs due to coherent reflection. The solution allows for decomposition of various sources of DPs in the model. In addition to the already described nonlinear-distortion and coherent-reflection mechanisms of DP generation, this study identifies a long-latency DPOAE component due to perturbation of nonlinear force. DP wavelets that are coherently reflected due to impedance irregularities travel toward the stapes across the primary generation region of DPs and there evoke perturbation of the nonlinear undamping force. The ensuing DP wavelets have opposite phase to the wavelets arising from coherent reflection, which results in partial cancellation of the coherent-reflection DP wavelets.
