Nonlinear Dynamic Behavior Research Articles

Size-dependent nonlinear dynamics of two-directional functionally graded microbeams in thermal environment under a moving mass

The size-dependent nonlinear dynamics of two-directional functionally graded (2D-FG) microbeams in a thermal environment under a moving mass is studied for the first time in the framework of the refined higher-order shear deformation theory (HSDT) and modified couple stress theory (MCST). The variation of the temperature-dependent material properties in the axial and thickness directions is estimated by the Mori–Tanaka homogenization scheme. Considering the rotary inertia and shear deformation, the nonlinear differential equations of motion, obtained from Hamilton’s principle, are discretized using an enriched beam element. Numerical results determined by the Newmark method in combination with Newton–Raphson iterative procedure confirm the efficiency of the derived beam formulation in predicting the nonlinear dynamics. The enriched beam element, which is derived herein by using hierarchical functions to enrich the conventional shape functions, is capable of furnishing accurate nonlinear dynamic characteristics with fewer elements compared to the conventional one. It is shown that the difference between the dynamic response predicted by the linear analysis and the nonlinear one increases by increasing the temperature, but it decreases by increasing the size scale parameter. The effects of the material gradation, temperature rise and micro-scale parameter on the nonlinear dynamic behavior of the 2D-FG microbeams are studied in detail and highlighted.

Non-linear dynamic behavior of T0 and T90 mesopelagic trawls based on the Hilbert–Huang transform

Although adopting the T90 mesh orientation on the trawl net can improve the selectivity of the trawl codend, it is unknown whether the T90 mesh orientation influences the dynamic behavior of the trawl system. Therefore, this study uses non-linear dynamic analysis to examine the effect of mesh orientations, mesh size, and twine diameter on the mesopelagic trawls' fluttering motions and hydrodynamic force responses. Three trawls are designed with different mesh orientations (T0 and T90), mesh sizes (40 mm and 60 mm), and twine diameters (0.96 mm and 1.11 mm) on the codend and codend extension sections of the trawl model based on Tauti's law. These trawls are tested in a flume tank under various flow velocities and catch sizes. A time-frequency analysis method based on the Hilbert–Huang transform is utilized to analyze each trawl's dynamic responses, including motions and drag force responses. The results are compared with those obtained through Fourier analysis using power spectral density. The results highlight that the oscillation amplitude of the surge motion of the T90 trawl is higher than that of the T0 trawl. In contrast, the T90 trawl's heave motion oscillation amplitude is smaller. The dominant frequency of the periodic high-energy coherent structures of the surge and heave motions are detected at a low frequency. The surge and heave motions of the T0 trawl have a greater response to the current components with lower frequencies than that of the T90 trawl. An increase in mesh size, a decrease in twine diameter, and a change in mesh orientation decrease the drag force. The inherent characteristic oscillations of the drag force response for the three trawl models are synchronized with the low-frequency characteristic of surge and heave motions. The gravity periods of the low-frequency mode components of drag force, surge motion, and heave motion for the T90 trawl are higher than those for the T0 trawls. In other words, the T90 trawl is more stable and selective than the T0 trawl. The findings of this study offer important information for comprehending and enhancing the selectivity of trawls in marine mesopelagic fisheries, particularly for exposing the effects of mesh orientation and design parameters on trawl performances.

Nonlinear Vibrations of Low Pressure Turbine Bladed Disks: Tests and Simulations

One of the most effective methods to limit the mechanical vibrations of bladed disks is the use of friction damping at mechanical joint interfaces. Unfortunately, dedicated tests to assess the impact of mistuning and the effectiveness of friction dampers are uncommon. This paper presents an original design of an academic demonstrator to perform an experimental analysis of the dynamic response of a tip-free bladed disk with under-platform dampers (UPDs), including an identification of intrinsic and contact mistuning introduced by the UPDs. The 48-blade disk was tested in a vacuum spinning rig by using permanent magnets. Vibration measurements were performed with the Blade Tip-Timing system. Tests were simulated using the Policontact tool, which predicted the average experimental nonlinear response in the presence of UPD, confirming the tool’s ability to capture the general nonlinear dynamic behavior of the mistuned bladed disk. This study presents a novel approach combining experimental Blade Tip Timing (BTT) with numerical simulations using Policontact (ver. 3.0) software and a model update based on experimental evidence to validate nonlinear dynamic responses. It distinguishes between intrinsic and contact mistuning effects, providing new insights into their impact on bladed disk vibrations. Additionally, a comparison of aluminum and steel UPDs reveals that steel offers a 26% greater damping efficiency due to its higher density and preload, significantly improving vibration reduction.

Research on rigid-flexible coupling nonlinear dynamics of light commercial vehicle considering frame flexibility

Commercial vehicles play a vital role in the transportation industry. Generally, there will present a complex nonlinear dynamic behavior composed of periodic, quasi-periodic, and even chaotic vibration in vehicle vertical system under the continuous speed bump excitation. To explore the nonlinear dynamic behavior of vehicle system, a new rigid-flexible coupling nonlinear dynamic model for light commercial vehicle has been developed theoretically with considering the frame flexibility, suspension stiffness and damping nonlinearity, and rubber bushing nonlinearity. The dynamic model for frame and suspension have been developed with discrete element method and lumped mass method, respectively. Then, the flexible frame model has been verified through the mode shape and frequency calculated by finite element simulation. And the rigid-flexible coupling nonlinear dynamic model of a light commercial vehicle has been verified with Adams simulation and testing results. Furthermore, the influence of vehicle speed and the height of speed bump, suspension stiffness and damping, as well as cargo weight and distribution on vehicle system dynamics is analyzed with bifurcation diagram, time history, frequency, phase diagram and Poincare section. The results show the significant and complex effects on the nonlinear vibration of vehicle system, especially the nonlinear damping and the flexible frame.

Mixed-mode oscillations and chaos in a complex chemical reaction network involving heterogeneous catalysis.

The nonlinear dynamical behavior in a complex isothermal reaction network involving heterogeneous catalysis is studied. The method first determines the multiple steady states in the reaction network. This is followed by an analysis of bifurcation continuations to identify several kinds of bifurcations, including limit point, Bogdanov-Takens, generalized Hopf, period doubling, and generalized period doubling. Numerical simulations are performed around the period doubling and generalized period doubling bifurcations. Rich nonlinear behaviors are observed, including simple sustained oscillations, mixed-mode oscillations, non-mixed-mode chaotic oscillations, and mixed-mode chaotic oscillations. Concentration-time plots, 2D phase portraits, Poincaré maps, maximum Lyapunov exponents, frequency spectra, and cascade of bifurcations are reported. Period-doubling and period-adding routes leading to chaos are observed. Maximum Lyapunov exponents are positive for all the chaotic cases, but they are also positive for some non-chaotic orbits. This result diminishes the reliability of using maximum Lyapunov exponents as a tool for determining chaos in the network under study.

Internal Resonance and Nonlinear Dynamics of an Axially Moving FGM Sandwich Cylindrical Shell

This paper provides an in-depth study of the resonant responses and nonlinear dynamics of a novel axially moving functionally graded material (FGM) sandwich cylindrical shell structure, specifically designed for supersonic aircraft operating under various complex environments. We present the derivation of the mechanical parameters and the nonlinear dynamic equations associated with this FGM sandwich cylindrical shell. By analyzing the natural frequencies of the structure, which is clamped at both ends, we identify the necessary parametric conditions for the nonlinear system to exhibit 1:2 internal resonance and 1:1 principal parameter resonance. To further investigate the resonant responses, we utilize the pseudo-arc length continuation method. In addition, the fourth-order Runge-Kutta algorithm is employed to examine the nonlinear dynamic behaviors of this system. This research explores the impacts of different external conditions, such as external excitation and aerodynamic force, on the resonant response and nonlinear dynamics of the axially moving FGM sandwich cylindrical shell. The results indicate that both external excitation and aerodynamic force have a significant influence on the nonlinear vibrations of this structure. Understanding these factors is important for optimizing the flight performance of supersonic vehicles in adverse environmental conditions.

On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system

This research work focuses on investigating the propagation of ultrasonic waves, which propagate mechanical vibrations of molecules or particles inside materials. Ultrasound imaging is extensively used and deeply rooted in the medical field. The key technologies that form the basis for many different uses in the area include transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, techniques for measuring blood flow and tissue motion, and three-dimensional imaging. The third-order non-linear β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. The exact solutions of different types, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted. These solutions are obtained by using two newly introduced techniques, namely modified generalized Riccati equation mapping method and modified generalized exponential rational function method. Moreover, breather, lump and other waves are extracted by the assistance of logarithmic transformation and different test functions. The used methodologies are extremely effective and possess substantial computing capacity to effectively address the different solutions with a high level of accuracy in these systems. The techniques used are well-known for being effective, simple, and flexible enough to integrate multiple soliton systems into a unified framework. In addition, we provide 2D and 3D graphs that explain the behavior of the solution at various parameter values, under the influence of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-fractional derivatives. The results offered in this study may improve the comprehension of the nonlinear dynamic behavior of the specific system and confirm the efficacy of the approaches used. We expect that our approaches will be beneficial for a wide range of nonlinear models and other problems in the related fields.

Nonlinear vibrations of three-phase composite truncated conical shells affected by complex factors under 1:1 internal resonance

The investigation into the nonlinear vibrations of the three-phase composite truncated conical shell structure is still in its early stages, which limits its practical implementation. This paper involves calculating equivalent physical property parameters for the three-phase composite materials and establishing a nonlinear dynamic model for the truncated conical shells. The study examines the nonlinear vibration characteristics of the shells under various conditions, considering factors such as temperature, humidity, reinforcement components, and external excitation. It is observed that temperature and humidity changes have significant influences on the structure's resonant responses, with varying effects for the driving mode and accompanying mode. The addition of GPLs or carbon fiber as reinforcement components weakens the resonant response amplitude with an increase in their content. External excitation is identified as a noteworthy energy input source that significantly impacts the nonlinear vibration characteristics of the three-phase composite conical shell structure, thereby amplifying the resonant responses and complicating the nonlinear dynamic behaviors. The findings hold significant value for guiding the design of advanced composite structures in future engineering.

Fractional-Order Modeling and Stochastic Dynamics Analysis of a Nonlinear Rubbing Overhung Rotor System

To study the nonlinear dynamic behavior and system stability of a rubbing overhung rotor with viscoelastic and memory-effect damping and random uncertain parameters, this paper introduces a fractional-order modeling and stochastic dynamic analysis method for the nonlinear overhung rotor system with frictional impact faults. Firstly, the dynamic equations of the overhung rotor considering friction effect and fractional damping effect are established based on the transfer matrix method and fractional order derivative. Then, the time-domain response of the fractional-order dynamic equations is solved by combining the Runge–Kutta method and the continuous fractional expansion, and the steady-state response characteristics of different fractional damping are analyzed in the deterministic case. Finally, to analyze the response of the system under the effect of stochastic parameters, the sparse grid-based PCE metamodel of the system response is developed. Statistical moments, probability distributions, and sensitivity indices of the response of stochastic systems are revealed. The results of this paper provide a theoretical basis for efficient and accurate prediction of the stochastic response of nonlinear rubbing overhung rotor systems.

Dynamic instability and nonlinear response analysis of nanocomposite sandwich arches with viscoelastic cores

This paper presents a comprehensive study of the nonlinear dynamic behavior and snap-through phenomena in sandwich arch structures with viscoelastic cores and carbon nanotube-reinforced nanocomposite face sheets. Subjected to uniform time-dependent pressure shocks, these arches exhibit complex snap-through behavior critical for practical engineering applications. Utilizing third-order shear deformation theory, the study accurately captures nonlinear behaviors. The viscoelastic core, modeled with the Kelvin-Voigt law, enhances damping and reduces vibration amplitudes. Numerical solutions are obtained using a Chebyshev-based Ritz method, Newmark integration, and Newton-Raphson method. The Budiansky-Ruth criterion evaluates dynamic buckling loads. Key findings include significant instability near buckling loads, increased buckling loads and vibration damping due to viscoelastic effects, reduced buckling loads with foam cores, improved performance with CNTs, and more pronounced CNT effects with greater deflections. Additional conclusions highlight the sensitivity of dynamic snap-through to geometric parameters and the superior accuracy of the proposed approach compared to traditional models. This research advances the understanding and design strategies for nonlinear sandwich arch structures, enhancing predictive capabilities in complex structural systems.

Analysis of the Nonlinear Complex Response of Cracked Blades at Variable Rotational Speeds

The operation of an aero-engine involves various non-stationary processes of acceleration and deceleration, with rotational speed varying in response to changing working conditions to meet different power requirements. To investigate the nonlinear dynamic behaviour of cracked blades under variable rotational speed conditions, this study constructed a rotating blade model with edge-penetrating cracks and proposes a component modal synthesis method that accounts for time-varying rotational speed. The nonlinear response behaviours of cracked blades were examined under three distinct operating conditions: spinless, steady speed, and non-constant speed. The findings indicated a competitive relationship between the effects of rotational speed fluctuations and unbalanced excitation on crack nonlinearity. Variations in rotational speed dominated when rotational speed perturbation was minimal; conversely, aerodynamic forces dominated when the effects of rotational speed were pronounced. An increase in rotational speed perturbation enhanced the super-harmonic nonlinearity induced by cracks, elevated the nonlinear damage index (NDI), and accentuated the crack breathing effect. As the perturbation coefficient increased, the super-harmonic nonlinearity of the crack intensified, resulting in a more complex vibration form and phase diagram.

Research on the complex dynamical behavior of H-bridge inverter with RLC load

Complex dynamical behaviors such as bifurcation and chaos exist in H-bridge inverter with RLC load, and these nonlinear behaviors will greatly increase the harmonic content of the output current and reduce the stability and reliability of the system. In this paper, a PI controller is added to widen the stable operation domain of the system. The stroboscopic mapping theory is used to model the system, the nonlinear dynamic behavior of the inverter is investigated by the bifurcation diagram, the folding diagram and the phase trajectory diagram are used for comparative verification, and the TDFC method is introduced to inhibit the chaotic behavior of the inverter, which further improves the stable range of the system operation. The fast-change stability theorem is used to analyze the stability of the system theoretically and verify the correctness of the numerical simulation. Therefore, the conclusions of the study provide a reliable theoretical basis for the design of the inverter system, which has important theoretical significance and practical value.

Analysis, Modelling and Simulation for the Intelligent Active Vibration Control of a Combined Plant using a New Gyroscopic Combined Actuator Model

There have been several research conducted worldwide on analysis, modelling, and controlling for flexible manipulator architectures. In this paper, one of the most interesting areas in the science of rotational dynamics as the study of spinning solid objects, such as Gyroscopes (G) has been investigated as a new approach for the improvement of the gyroscope non-linear behaviour which controls the magnitude and the direction of the torque separately in the frequency domain by describing a New Graphical Combined Actuator Model (NGCAM) for the Intelligent Active Vibration Control (IAVC) of a Combined Plant (CP) as a linear-nonlinear combined single link Robotics Flexible Manipulator (RFM) structure which rotates in the horizontal plane with two degrees of freedom in order to have a performance assessment and suppressing vibrations. The effect of the parameter variation on the stability and dynamic nonlinear behaviour of the gyroscope in gimbals with a feedback sensor control system has been formed and optimized by the Modified Fuzzy Logic (MFL) algorithm as an artificial intelligence control technique and the Proportional, Integral and Derivative (PID) tuning by the modified Ziegler Nichols (ZN) method. To validate the gyroscope stabilization to be implemented into the RFM for controlling the vibration, the proposed method combines Active Force Control (AFC) technique with Fuzzy Logic (FL) and PID as the (AVC-FL-PID) controller for the NGCAM, CP and RFM by using MATLAB & SIMULINK program is created. For a linear-non-linear combination system, it is better to use a linear-non-linear combination controller. Simulation results illustrate the effectiveness of the proposed strategy which is significantly and quite satisfactory about 25 (%) generally better than compared to the other systems’ performance criteria and is so clear and significant optimization is visible than compared to the other conventional actuators such as PZTs and other control strategies in improvement stabilization and vibration control of RFM structures. The advantages of the proposed method and the possibilities of further improvements are discussed.

Nonlinear behavior and energy harvesting performance of a new tunable quasi-zero stiffness system.

Energy harvesting from vibrations is a popular research topic. However, it is difficult to change the values of its dynamic stiffness characteristics during the operation of device. This paper analyzes the nonlinear dynamical behavior and energy harvesting performance of an energy harvesting device with a gear unit and an inertial amplifier. The Melnikov method is used to discriminate the chaos behavior of the system and is illustrated by numerical simulations. Chaotic dynamics analysis provides a simplified analytical idea that offers more insight into the performance of this energy harvesting device. In addition, the basins of attraction of the coexistence solution of the system are plotted, and the trajectory and energy harvesting efficiency of the system are analyzed for changes in the initial value. The results show that the device has the convenience to change the form and efficiency of system energy harvesting. The theory of Melnikov functions recognizes the presence of chaos and can provide solutions for the parameterization of the system. The choice of initial value greatly affects the energy harvesting efficiency.

Evaluating dynamic models for rigid-foldable origami: unveiling intricate bistable dynamics of stacked-Miura-origami structures as a case study.

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass-spring-damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Nonlinear dynamic behaviors of a shaft-bearing-pedestal system with outer ring slip and damage

Nonlinear dynamic behaviors of a shaft-bearing-pedestal system with outer ring slip and damage

Exploring nonlinear dynamics in brain functionality through phase portraits and fuzzy recurrence plots.

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.

The Time Series Classification of Discrete-Time Chaotic Systems Using Deep Learning Approaches

Discrete-time chaotic systems exhibit nonlinear and unpredictable dynamic behavior, making them very difficult to classify. They have dynamic properties such as the stability of equilibrium points, symmetric behaviors, and a transition to chaos. This study aims to classify the time series images of discrete-time chaotic systems by integrating deep learning methods and classification algorithms. The most important innovation of this study is the use of a unique dataset created using the time series of discrete-time chaotic systems. In this context, a large and unique dataset representing various dynamic behaviors was created for nine discrete-time chaotic systems using different initial conditions, control parameters, and iteration numbers. The dataset was based on existing chaotic system solutions in the literature, but the classification of the images representing the different dynamic structures of these systems was much more complex than ordinary image datasets due to their nonlinear and unpredictable nature. Although there are studies in the literature on the classification of continuous-time chaotic systems, no studies have been found on the classification of discrete-time chaotic systems. The obtained time series images were classified with deep learning models such as DenseNet121, VGG16, VGG19, InceptionV3, MobileNetV2, and Xception. In addition, these models were integrated with classification algorithms such as XGBOOST, k-NN, SVM, and RF, providing a methodological innovation. As the best result, a 95.76% accuracy rate was obtained with the DenseNet121 model and XGBOOST algorithm. This study takes the use of deep learning methods with the graphical representations of chaotic time series to an advanced level and provides a powerful tool for the classification of these systems. In this respect, classifying the dynamic structures of chaotic systems offers an important innovation in adapting deep learning models to complex datasets. The findings are thought to provide new perspectives for future research and further advance deep learning and chaotic system studies.

Nonlinear dynamic analyses of sandwich porous FG cylindrical shells with dual-layered FG porous cores

This research examines the nonlinear vibrations and dynamic postbuckling (DPB) analyses of sandwich porous functionally graded (SPFG) cylindrical shells with dual-layered FG porous (FGP) cores exposed to external excitation, using a semi-analytical method. The study investigates two types of FG layers: one with evenly distributed porosities (FG-EPD) and another with unevenly distributed porosities (FG-UEPD). It also studies the FGP cores in four configurations: one featuring symmetric porosity distribution with stiffening in the surface areas (SPD-Stiff), another with softening in the surface areas (SPD-Soft), a third with nonsymmetric porosity distribution (NSPD), and a fourth with uniform porosity distribution (UPD). Therefore, the SPFG cylindrical shells with dual-layered FGP cores with eight different configurations are investigated. Utilizing the classical shell theory (CST) alongside the geometrical nonlinearity in von Kármán–Donnell framework, and Galerkin’s method, this study addresses the nonlinear dynamic problem. An approximate solution for the deflection shape using three terms is selected, and the relationship between frequency and amplitude in nonlinear vibration is clearly defined. The nonlinear dynamic behaviors including vibration and DPB responses are examined using the P-T method, which is named for its use of the piecewise constant argument in conjunction with the Taylor series expansion. The critical dynamic buckling load of SPFG cylindrical shells with dual-layered FGP cores is investigated via the Budiansky–Roth criterion.

Exploring Nonlinear Dynamics In Brain Functionality Through Phase Portraits And Fuzzy Recurrence Plots.

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.