Mechanical systems with inherent chaotic behavior are of notable practical interest due to their applicability in many fields of technology, from industrial mills and concrete mixers to microscopic micromechanical random bit generators. One of the mo...
Analysis and controlling of bifurcation for a class of chaotic Van der Pol- Duffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical va...
This paper mainly studied the analytical solutions of three types of Van der Pol-Duffing equations. For a system with parametric excitation frequency, we knew that the ordinary homotopy analysis method would be unable to find the analytical solution....
The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Tradi...
This paper presents a comprehensive framework for the identification, state estimation, and robust control of a bistable Duffing–Holmes oscillator, validated through an experimental setup. First, to address parametric uncertainty, a Recursive L...
The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order s...
This paper establishes the existence, uniqueness, and Ulam–Hyers stability of solutions for a novel class of coupled sequential hybrid Hilfer fractional q-Duffing equations. By integrating Dhage’s hybrid structure with generalized Hilfer...
Fractional-order models provide a powerful framework for capturing memory-dependent and viscoelastic dynamics in mechanical systems, which are often inadequately represented by classical integer-order characterizations. This study addresses the ident...
In the process of dynamic Measurement While Drilling (MWD), the strong vibration and rapid rotation of the Bottom Hole Assembly (BHA) lead to multi-frequency and high-amplitude noise interference in the attitude measurement signal. The weak original...
Over the past century, a tremendous amount of work on the Duffing system has been done with continuous external force, including analytical and numerical solution methods, and the dynamic behavior of physical systems. However, hows does the Duffing o...
In coal mine non-solidly grounded systems, high-impedance faults generate minimal zero-sequence currents with obscured characteristics and strong interference, complicating faulted line identification. Existing methods rarely address three-phase imba...
In this paper, the abundant nonlinear dynamical behaviors of a fractional-order time-delayed Duffing system under harmonic excitation are studied. By constructing Melnikov function, the necessary conditions of chaotic motion in horseshoe shape are de...
As the non-solid-earthed network fails, the zero-sequence current of each line is highly non-stationary, and the noise component is serious. This paper proposes a fault line selection method based on modified complementary ensemble empirical mode dec...
Burkholderia glumae are bacteria pathogenic to rice plants that cause a disease called bacterial panicle blight (BPB) in rice panicles. BPB, induced by B. glumae, causes enormous economic losses to the rice agricultural industry. B. glumae also cause...
Aiming at the problems of the low detection accuracy and difficult identification of the early weak fault signals of rolling bearings, this paper proposes a method for detecting the early weak fault signals of rolling bearings based on a double-coupl...
This study investigates stochastic bifurcation in a generalized tristable Rayleigh–Duffing oscillator with fractional inertial force under both additive and multiplicative recycling noises. The system’s dynamic behavior is influenced by its inherent...
In the process of drilling, severe downhole vibration causes attitude measurement sensors to be erroneous; the errors will accumulate gradually during the inclination calculation. As a result, the ultimate well path could deviate away from the planne...
By introducing a switching scheme related to the state and time, a typical switched model alternating between a Duffing oscillator and van der Pol oscillator is established to explore the typical dynamical behaviors as well as the mechanism of the sw...
This paper is concerned with the design of synchronized large-scale chaos random number generators (CRNGs) and its application to secure communication. In order to increase the diversity of chaotic signals, we firstly introduce additional modulation...
Islanding occurs when a load is energized solely by local generators and can result in frequency and voltage instability, changes in current, and poor power quality. Poor power quality can interrupt industrial operations, damage sensitive electrical...
Time-delay chaotic systems can have hyperchaotic attractors with large numbers of positive Lyapunov exponents, and can generate highly stochastic and unpredictable time series with simple structures, which is very suitable as a secured chaotic source...
Based on the principles of nonlinear dynamics, a dynamic model of the jet system for adaptive fire-fighting monitors was established. The influence of nonlinear fluid spring force on the dynamic model was described by the Duffing equation. Results of...
The paper considers a rotor system with a nonlinear characteristic. Its equations of motion are a kind of Duffing class equations with multiple degrees of freedom. The paper shows the advantage of using the method of elliptic functions for solving pr...
This study investigates the effect of a nonlinear saturation controller (NSC) on the van der Pol–Mathieu–Duffing oscillator (VMDO). The oscillator is a single degree of freedom (DOF) system. It is driven by an external force. It is descri...
Heartbeat rhythms are related to a complex dynamical system based on electrical activity of the cardiac cells usually measured by the electrocardiogram (ECG). This paper presents a mathematical model to describe the electrical activity of the heart t...
Common upper limb peripheral artery diseases (PADs) are atherosclerosis, embolic diseases, and systemic diseases, which are often asymptomatic, and the narrowed arteries (stenosis) will gradually reduce blood flow in the right or left upper limbs. Up...
The proposed framework is based on a path-dependent entropic variational construction for nonlinear damped vibration systems. Accumulated mechanical spending and heat-transfer power are represented as history contributions to the action. Each irrever...
As crucial equipment during industrial manufacture, the health status of rotating machinery affects the production efficiency and device safety. Hence, it is of great significance to diagnose rotating machinery faults, which can contribute to guarant...
Many mechanical systems manifest nonlinear behavior under nonstationary random excitations. Neglecting this nonlinearity in the modeling of a dynamic system would result in unacceptable results. However, it is challenging to find exact solutions to n...
This study investigates the multistability phenomenon and coexisting attractors in the modified Autonomous Van der Pol-Duffing (MAVPD) system and its fractional-order form. The analytical conditions for existence of periodic solutions in the integer-...
Metamaterials (MTMs) based on a periodic array of resonant coils have been shown to behave as μ-negative (MNG), enabling the focusing of magnetic flux. The phenomenon has been deployed by designers to boost the efficiency of many inductively coupled...
In engineering design, oftentimes a system’s dynamic response is known or can be measured, but the source generating these responses is not known. The mathematical problem where the focus is on inferring the source terms of the governing equati...
The aim of this work is to model the nonlinear dynamics of conservative oscillators, with restoring force originating from even-order potentials. In particular, we extend our previous findings on inverting the time-integral equation that arises in th...
Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unid...
DUF538 proteins belong to a large group of uncharacterized protein families sharing the highly conserved Domain of Unknown Function (DUF). Attention has been given to DUF538 domain-containing proteins due to changes in their gene expression behavior...
DUF966 genes are widely found in monocotyledons, dicotyledons, mosses, and other species. Current evidence strongly suggests that they are involved in growth regulation and stress tolerance in crops. However, their functions in cucumbers remain unexp...
In the paper, we first develop a novel automatically energy-preserving scheme (AEPS) for the undamped and unforced single and multi-coupled Duffing equations by recasting them to the Lie-type systems of ordinary differential equations. The AEPS can a...
As the human population grows rapidly, food shortages will become an even greater problem; therefore, increasing crop yield has become a focus of rice breeding programs. The maize gene, ZmDUF1645, encoding a putative member of the DUF1645 protein fam...
Two nonlinear Duffing equations are numerically treated in this article. The nonlinear fractional-order Duffing equations and the second-order nonlinear Duffing equations are handled. Based on the collocation technique, we provide two numerical algor...
In this paper, we discuss the averaging method for periodic systems of second order and the behavior of solutions that intersect a hyperplane. We prove an averaging theorem for impact systems. This allows us to investigate the approximate dynamics of...
As a powerful feature extraction tool, a convolutional neural network (CNN) has strong adaptability for big data applications such as bearing fault diagnosis, whereas the classification performance is limited when the quality of raw signals is poor....
Sensors based on chaotic oscillators have a simple design, combined with high sensitivity and energy efficiency. Among many developed schemes of such sensors, the promising one is based on the Duffing oscillator, which possesses a remarkable property...
The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the...
Classical periodic solution theories of undamped Duffing equations are mostly restricted to continuous nonlinearities, while discontinuous models from mechanical impact and switching circuits lack systematic existence criteria for crossing periodic o...
In this investigation, two different models for two coupled asymmetrical oscillators, known as, coupled forced damped Duffing oscillators (FDDOs) are reported. The first model of coupled FDDOs consists of a nonlinear forced damped Duffing oscillator...
Millimeter-wave technology helps achieve antenna miniaturization and high gain, but it is limited by factors such as short wavelength, high transmission loss, and high signal-to-noise ratio, which put higher requirements on the accuracy and computing...
The aim of this paper focuses on finding equivalent representation forms of forced, damped, two degree-of-freedom, nonlinear systems in the sense of Lyapunov by using a nonlinear transformation approach that provides decoupled, forced, damped, nonlin...
This paper presents the dynamic behaviors of a second-order asymmetric stochastic delay system with a Duffing oscillator as well as through the detection of weak signals, which are analyzed theoretically and numerically. The dynamic behaviors of the...
The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose dynamics are similar to those of bistable mechanical systems, such as Euler arches and Duffing oscillators. Of part...
The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose long-term conformational dynamics are similar to the dynamics of bistable mechanical systems such as Euler arches a...
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