In this paper, the dynamic behavior of the van der Pol-Rayleigh system is studied by using the fast–slow analysis method and the transformation phase portrait method. Firstly, the stability and bifurcation behavior of the equilibrium point of t...
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 i...
Ensuring noise immunity is one of the main tasks of radio engineering and telecommunication. The main task of signal receiving comes down to the best recovery of useful information from a signal that is destructed during propagation and received toge...
In this study, different standard frequency analysis (FA) methods are applied to measured leaf temperature data of maize plants (developmental stages EC13–15). These FA methods are used to identify specific behaviors, regularities, and sudden c...
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...
The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities in the Itô sense, which can further help researchers understand the propagation of soliton nonlinear syst...
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized
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...
This article presented a formal systematic transformation of the complex coupled Kairat-Zhaidary-Myrzakulov system (KZMS) into a single ordinary differential equation (ODE), with the aim of providing a complete dynamical picture of the system that go...
Poisoning and shilling attacks remain a serious threat to recommender systems, especially as attackers increasingly mimic plausible profile statistics. This paper proposes an architecture-independent behavioral detection layer that models user intera...
This paper explores the exact solutions of the fractional Hirota–Satsuma coupled KdV (fHScKdV) equation in the Beta fractional derivative. The logistic method is first proposed to construct analytical solutions for the fHScKdV equation. In orde...
The main purpose of this article is to investigate the dynamic behavior and optical soliton for the M-truncated fractional paraxial wave equation arising in a liquid crystal model, which is usually used to design camera lenses for high-quality photog...
This study aims to investigate various dynamical aspects of the dual-mode Gardner equation derived from an ideal fluid model. By applying a specific wave transformation, the model is reduced to a planar dynamical system, which corresponds to a conser...
This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical sy...
In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable...
This research explores the dynamic characteristics of the soliton neuron model, a mathematical approach used to describe various complicated processes in neuroscience, including the unclear mechanisms of numerous anesthetics. An appropriate wave tran...
In this work, quasi-periodic and periodic vibration responses of an axially moving beam are analytically investigated under multiple-frequency excitation. The governing equation is transformed into a nonlinear differential equation by applying the Ga...
This paper investigates the bifurcation, phase portrait, and traveling wave solutions of the Aizhan–Gudekli–Nurshuak–Zhanbota equation. By performing a simple linear transformation on the solution of the equation and applying the tr...
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space
A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it po...
The paper examines the task of managing the finances of a company with branches when funds are saved on the central company account, from which payments for the expenses of the branches are made. The dynamics of these expenses may have similar dynami...
This study explores the novel dynamics of the (3+1)-dimensional generalized Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A Galilean transformation is employed to derive the associated system of equations. Perturbing this...
The main object of this paper is to study the traveling wave solutions of the fractional coupled Konopelchenko–Dubrovsky model by using the complete discriminant system method of polynomials. Firstly, the fractional coupled Konopelchenko–...
This work investigates the dynamical properties of the Kolmogorov–Petrovskii–Piskunov (KPP) equation. We begin by establishing its non-integrability through the Painlevé test. Using a traveling wave transformation, we reduce the eq...
Covariant integral quantization with rotational
This paper examines the (2 + 1)-dimensional complex modified Korteweg–de Vries equation, which describes the intricate motion of water particles from the surface to the bottom. By applying an appropriate wave transformation that reduces the gov...
This work investigates the optical soliton solutions and their dynamical behaviors of the fractional stochastic Biswas–Arshed equation (FSBAE). By employing the definition of truncated M-fractional derivative and a wave transformation, we reduc...
In this study, we examine the bifurcations and dynamics of a piecewise linear van der Pol equation—a model that captures self-sustained oscillations and is applied in various scientific disciplines, including electronics, neuroscience, biology,...
This article explores the generalized Gerdjikov–Ivanov equation describing the propagation of pulses in optical fiber. The equation studied has a variety of applications, for instance, in photonic crystal fibers. In contrast to the classical Ge...
In this study, novel exact solutions of the Duffing equation with their phase portraits are proposed and reasoned. It is shown that phase trajectories are initially elliptical and become distorted in the unstable area with the growth of the variable...
The present work is attentive to studying the qualitative analysis for a nonlinear strain wave equation describing the finite deformation elastic rod taking into account transverse inertia, and shearing strain. The strain wave equation is rewritten a...
The fourth-order nonlinear Boussinesq water wave equation, which describes the propagation of long waves in the intertidal zone, is investigated in this study. The exact wave patterns of the equation were computed using the
This paper presents a circuit design methodology for the analog realization of time-varying fractional-order chaotic systems. While most existing studies implement such systems by switching between two or more constant fractional orders, these approa...
In this research, we study a dynamical system of total nitrogen transformation in a mangrove-filled constructed wetland. The system’s variables are the mangrove biomass concentration and total nitrogen concentration in wastewater and in soil solution...
In this paper, we study the time-space truncated M-fractional model of shallow water waves in a weakly nonlinear dispersive media that characterizes the nano-solitons of ionic wave propagation along microtubules in living cells. A fractional wave tra...
In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurc...
This paper presents a stability analysis for droop-based islanded AC microgrids via an autonomous shooting method based on bifurcation theory. Shooting methods have been used for the periodic steady-state analysis of electrical systems with harmonic...
This work examines the nonlinear dynamics of a generalized Korteweg–de Vries–Zakharov–Kuznetsov equation, a model that appears in plasma physics, shallow water flows, and nonlinear wave propagation. By applying a solitary-wave trans...
An examination was previously derived to conclude the understanding of the response of a cantilever beam with a tip mass (CBTM) that is stimulated by a parameter to undergo small changes in flexibility (stiffness) and tip mass. The study of this prob...
The central objective of this study is to develop some different wave solutions and perform a qualitative analysis on the nonlinear dynamics of the time-fractional chiral nonlinear Schrodinger’s equation (NLSE) in the conformable sense. Combine...
This paper proposes a method for examining chaotic structures in semiconductor or alloy voltage oscillation time-series, and focuses on the case of the TlInTe2 semiconductor. The available voltage time-series are characterized by instabilities in neg...
This paper proposes the generalized modified unstable nonlinear Schrödinger’s equation with applications in modulated wavetrain instabilities. The extended direct algebra and generalized Ricatti equation methods are applied to find innovat...
In this study, the complete discrimination system for the polynomial method (CDSPM) is employed to analyze the integrable Gardner Equation (IGE). Through a traveling wave transformation, the model is reduced to a nonlinear ordinary differential equat...
This study employs spatial optimization principles to investigate the nonlinear vibration of a flexibly supported Euler–Bernoulli beam, a (1 + 1)-dimensional system subjected to axial loads. The modified Khater method, a crucial tool in mechani...
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 trans...
In this article, the modified
Brake-induced steering wheel shimmy is a critical nonlinear dynamic phenomenon that severely compromises vehicle handling stability and driving safety. While clearances in steering mechanism kinematic pairs are widely recognized as a primary cause of...
In this study, an analytical and dynamical study of the classical Kolmogorov–Petrovsky– Piskunov (KPP) equation is carried out by means of the improved generalized Riccati equation mapping (IGREM) method. An appropriate traveling-wave tra...
Protecting medical images requires encryption methods that combine cryptographic key management with validated nonlinear transformations and effective diffusion mechanisms. This study proposes an encryption-instance-specific framework based on a CSPR...
In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaoti...
of 2