In this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-Hamiltonian system by using expansions of the first order Melnikov functions. We give a method to compute more coefficients of the expansions to find more limit c...
This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m. By analyzing the asymptotic expansion (AE) of t...
This paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither para...
The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possibl...
When aiming to cut down on the emission of nitric oxides by gas turbine engines, it is advantageous to have them operate at low combustion temperatures. This is achieved by lean premixed combustion. Although lean premixed combustion is a proven and p...
The study aims at investigating a new fundamental property of infectious diseases with natural adaptive immunity that weakens over time—qualitative change (bifurcation) in the behavior of the “virus vs. human” system with an increas...
This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) te...
This article establishes a nonlinear flutter system for a long-span suspension bridge, aiming to analyze its supercritical flutter response under the influence of nonlinear aerodynamic self-excited force. By fitting the experimental discrete values o...
In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 . W...
In this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles. For the first class of systems, there exist 2n+1 limit cycles, which include an algebraic...
In this paper, a class of quintic systems is investigated. The first 13 focal values are computed with the aid of MATHEMATICA. Then the necessary conditions of integrability and linearizability are obtained and the sufficiency of every condition is p...
We search for limit cycles in the dynamical model of two-species chemical reactions that contain seven reaction rate coefficients as parameters and at least one third-order reaction step, that is, the induced kinetic differential equation of the reac...
The bifurcation of limit cycles is an important part in the study of switching systems. The investigation of limit cycles includes the number and configuration, which are related to Hilbert’s 16th problem. Most researchers studied the number of...
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonia...
In recent years, there has been considerable interest in the study of feedback systems containing processes whose dynamics are best described by fractional order derivatives. Various situations have been cited for describing heat flow and aspects of...
We provide the maximum number of limit cycles for continuous and discontinuous planar piecewise differential systems formed by linear Hamiltonian saddles and separated either by one or two parallel straight lines. We show that when these piecewise di...
In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and...
This paper focuses on investigating the bifurcation of limit cycles and centers within a specific class of three-dimensional cubic systems possessing Z3-equivariant symmetry. By calculating the singular point values of the systems, we obtain a necess...
In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the...
In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs) in n-dimensional piecewise-smooth dynam...
In this paper, we study the number of limit cycles of a new class of polynomial differential systems, which is an extended work of two families of differential systems in systems considered earlier. We obtain the maximum number of limit cycles that b...
This paper reports the finding of unstable limit cycles and singular attractors in a two-dimensional dynamical system consisting of an inductor and a bistable bi-local active memristor. Inspired by the idea of nested intervals theorem, a new programm...
The 2×2 game is the simplest non-trivial model of strategic interaction: there are two players, each has two strategies, and each has a strict preference ranking over the four possible outcomes. For models of play that depend only on the rankin...
In many problems appearing in applied mathematics in the nonlinear ordinary differential systems, as in physics, chemist, economics, etc., if we have a differential system on a manifold of dimension, two of them having a first integral, then its phas...
The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models. Consequently, attempts to solve Hilbert’s sixteenth problem...
In this paper, we investigate the maximum number of small-amplitude limit cycles bifurcated from a planar piecewise smooth focus-parabolic type cubic system that has one switching line given by the x-axis. By applying the generalized polar coordinate...
A WHO and UNICEF joint report states that in 2008, 884 million people lacked access to potable drinking water. A life-cycle approach to develop potable water systems may improve the sustainability for such systems, however, a review of the literature...
In this paper, very high cycle fatigue (VHCF) strengths are first evaluated for the TC17 titanium alloy and the welding joint of the 6005A-T6 aluminum alloy using the up-and-down method (UDM) and continuous testing method (CTM). Then, the influence o...
In this paper we develop an approach for obtaining the solutions to systems of linear retarded and neutral delay differential equations. Our analytical approach is based on the Laplace transform, inverse Laplace transform and the Cauchy residue theor...
In this study, we developed a new methodology to analyze the off-design performance of the organic Rankine cycle. The methodology enabled us to predict the performance based on four-dimensional decision variables and a set of constraints. A correspon...
The soil–water characteristic curve (SWCC) is a key input for the numerical simulation of geotechnical engineering. It contains the basic information needed to describe the mechanical behavior of unsaturated soil. In order to study the variatio...
In this article, we explore a new extended Lienard-type planar system with “corrections” of the second kind Chebyshev’s polynomial Un. The number and type of limit cycles are also studied. The discussion on the y(t)—component...
Systems composed of piecewise smooth differential (PSD) mappings have quantitatively been searched for answers to a substantial issue of limit cycle (LC) bifurcations. In this paper, LC numbers (LCNs) of a PSD system (PSDS) consisting of four regions...
Time integration is commonly used to obtain accurate system responses, such as the limit cycle oscillations (LCOs) for an aeroelastic system with freeplay. However, the integrations that start with various initial conditions (I.C.s) are usually studi...
This paper applies numerical continuation techniques to a nonlinear aeroelastic model of a highly flexible, high-aspect-ratio wing. Using continuation, it is shown that subcritical limit cycle oscillations, which are highly undesirable phenomena prev...
In this paper, a synthetic jet actuators (SJA)-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO) in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled exte...
Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investiga...
The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of p...
Curve squeal is a highly disturbing tonal noise produced by railway vehicles on tight curves, primarily attributed to lateral sliding at the wheel–rail interface. An essential step to estimate curve squeal noise levels is to determine the nonli...
Cantilever-type rotating bending fatigue tests were conducted under a very high cycle fatigue regime using conventionally manufactured Ti-6Al-4V specimens having drilled artificial defects with different sizes. The relationship between fatigue limit...
This paper investigates the flutter characteristics of composite laminates in hypersonic yawed flow using numerical simulations. The governing equations are derived based on Hamilton’s principle and were discretized using the assumed mode metho...
A laboratory-scale atomic layer deposition (ALD) reactor system model is derived for alumina deposition using trimethylaluminum and water as precursors. Model components describing the precursor thermophysical properties, reactor-scale gas-phase dyna...
A non-smooth switched harvest on predators is introduced into a simple predator-prey model with logistical growth of the prey and a bilinear functional response. If the density of the predator is below a switched value, the harvesting rate is linear;...
While the estimation of the critical velocity for fluidelastic instability of tube arrays has received considerable attention for decades, the studies intended to analyze the post-stable behavior have been scarce. However, the behavior of the system...
This paper is devoted to local bifurcations of three-dimensional (3D) quadratic jerk system. First, we start by analysing the saddle-node bifurcation. Then we introduce the concept of canonical system. Next, we study the transcritial bifurcation of c...
To improve the mechanical and durability properties of low liquid limit soil, an eco-friendly, all-solid, waste-based stabilizer (GSCFC) was proposed using five different industrial solid wastes: ground granulated blast-furnace slag (GGBS), steel sla...
The very high cycle fatigue (VHCF) property of TC21 titanium alloy blunt-notched specimens were investigated by using an ultrasonic fatigue test machine with a frequency of 20 kHz. S–N of blunt-notched specimens illustrated a continuous decreas...
We present a new discontinuous ordinary differential equation (ODE) model of the glacial cycles. Model trajectories flip from a glacial to an interglacial state, and vice versa, via a switching mechanism motivated by ice sheet mass balance principles...
Planar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has...
A general approach for the analysis and design of self-oscillating resonant converters is presented in this paper, for a particular class of circuits in which the change of input voltage polarity is caused by the zero-crossings of the input inductor...
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