Article
Engineering, Multidisciplinary
Changjin Xu
Summary: Based on previous publications, a new fractional-order chaotic finance model is established, and the chaotic control for the considered model is studied. Stability and bifurcation conditions are established using the stability criterion and Hopf bifurcation knowledge of fractional order differential dynamical system. The role of delay in controlling the stability and Hopf bifurcation for the model is fully reflected. Numerical simulation figures and bifurcation plots support the established primary conclusions.
AIN SHAMS ENGINEERING JOURNAL
(2022)
Article
Mathematics
Xinxin Qie, Quanbao Ji
Summary: This study investigated the stability and bifurcation of a nonlinear system model, finding that the system underwent two supercritical bifurcations and also observing saddle-node and torus bifurcations. Numerical simulations were carried out to validate the proposed approach.
Article
Physics, Mathematical
Eddie Nijholt, Tiago Pereira, Fernando C. Queiroz, Dmitry Turaev
Summary: We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. We give general conditions for the existence of chaotic network dynamics under homogeneous diffusive coupling for any network configuration. Our method is based on the theory of local bifurcations developed for diffusively coupled networks. In particular, we introduce the class of versatile network configurations and prove that the Taylor coefficients of the reduction to the center manifold can take any given value for any versatile network.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Xiaoyan Hu, Bo Sang, Ning Wang
Summary: In this work, a five-parameter jerk system with a hyperbolic sine nonlinearity is analyzed. The symmetrical and asymmetrical cases are studied, and the bifurcations are determined using analytical methods. The discovery of chaotic motion mechanisms in jerk systems is the main contribution of this work. Circuit simulations are used to validate the numerical results.
Article
Engineering, Mechanical
Amira Amamou
Summary: Floating ring bearings are commonly used in automotive turbocharger rotors due to their improved damping and emergency-operating capabilities. Nonlinear vibration effects induced by self-excited oscillations from bearing oil films may lead to rotor damage, but an understanding of the system's characteristics can aid in designing and safely operating rotating machines.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE
(2022)
Article
Engineering, Mechanical
V Eclerova, L. Pribylova, A. E. Botha
Summary: Nonlinear problems involving phases are common in applied mathematics and physics, and pose a challenge for numerical analysis. This paper proposes a method to transform these problems into structurally stable generalized systems, allowing for easier analysis using standard numerical continuation techniques. The method involves replacing harmonic terms with supercritical Hopf bifurcation normal form subsystems to achieve structural stability. The approach is illustrated using the ac-driven, Stewart-McCumber model of a single Josephson junction, and the findings show the presence of a two-parameter Hopf-Hopf bifurcation and its connection to the Neimark-Sacker bifurcation of limit cycles. The results also provide a complete understanding of the overlapping Arnold tongues and their relation to the Shapiro steps observed in the junction's current-voltage characteristics.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Chengdai Huang, Huanan Wang, Jinde Cao
Summary: This paper presents novel results on fractional order-induced bifurcation of a tri-neuron fractional-order neural network (FONN) with delays and instantaneous self-connections. The authors systematically analyze the order as a bifurcation parameter and establish the order critical value through an implicit function array. The derived results show that once the fractional order exceeds the bifurcation critical value, the system's stability is destroyed and Hopf bifurcation occurs. Two numerical experiments are conducted to validate the developed key findings.
Article
Mathematics, Applied
Hua Zhang, Jianjun Paul Tian, Ben Niu, Yuxiao Guo
Summary: This paper investigates a two-dimensional tumor-immune model with time delay in the adaptive immune response, showing through qualitative and numerical analysis the impact of the immune system on tumors. The positive equilibrium is locally asymptotically stable when the ratio of immune killing rate to tumor volume growth rate is less than a critical value. The results suggest that the time taken for the adaptive immune system to respond to tumors can lead to oscillation dynamics and impact patient survival time.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Mechanical
Erxi Zhu, Min Xu, Dechang Pi
Summary: This paper presents a new method for anti-control of Hopf bifurcation in high-dimensional chaotic systems and verifies it through simulation results.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Paul A. Meehan
Summary: Research shows that chaotic instability in brake squeal is caused by mode coupling instability via friction. Conservative analytical conditions were developed and numerically verified for suppressing brake squeal chaos. The results provide predictive insight into conditions under which brake squeal chaos occurs and its suppression.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Multidisciplinary
A. M. A. El-Sayed, S. M. Salman, A. M. A. Abo-Bakr
Summary: The Henon map, introduced by Henon, is a rich dynamical model that has been compared with other dynamical systems. In this study, we investigate the dynamics of the difference equation with continuous arguments corresponding to the Henon map and its singularly perturbed counterpart. We analyze the local stability of fixed points and observe various types of bifurcation. Theoretical analysis is confirmed through numerical simulations, showcasing the complex dynamics of the system.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Computer Science, Interdisciplinary Applications
J. Alidousti, Z. Eskandari
Summary: This paper investigates the dynamic behavior of a fractional governor system, studying its stability, bifurcation, and Hopf bifurcation conditions. The results obtained differ from classical models, and chaos tendency in non-autonomous systems is explored using bifurcation diagrams and Poincare maps analysis. Numerical results are provided to illustrate theoretical findings, which can be applied as technical tools for control and rotary machine designers.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Binhao Hong, Chunrui Zhang
Summary: In this paper, the dynamical behavior of a predator-prey model with discrete time is explored through theoretical analysis and numerical simulation. The existence and stability of four equilibria are analyzed, with Flip bifurcation and Hopf bifurcation occurring at the unique positive equilibrium point. Chaotic cases are observed at some corresponding internal equilibria when small perturbations are applied to the bifurcation parameter. Numerical simulations using maximum Lyapunov exponent and phase diagrams reveal a complex dynamical behavior.
Article
Mathematics, Applied
Marcos C. Mota, Regilene D. S. Oliveira
Summary: This paper studies the quadratic system (x) over dot = yz, (y) over dot = x - y, (z) over dot = 1 - x(alpha y + beta x), and introduces the Sprott BC system. It analyzes the system's dynamics at different parameter values and demonstrates a Hopf bifurcation at α = 0.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)
Article
Mechanics
Fanrui Wang, Haozhe Liu, Zhouchao Wei, Irene Moroz
Summary: This work discusses the generalized Hopf bifurcation analysis of a piecewise-smooth wheel system with higher order discontinuities, using center manifold reduction to simplify the system and considering non-smooth factors. The analysis can be divided into two cases based on the coefficient of the quadratic term, with the bifurcation type determined by the stability of the first-order fine focus or by constructing a Poincare map. Additionally, a convenient method to judge bifurcation types is proposed due to the symmetrical characteristic of the wheel system, with numerical simulations demonstrating the feasibility of theoretical analysis.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2021)
Article
Physics, Multidisciplinary
Muhammad Aqeel, Salman Ahmad, Anam Azam, Faizan Ahmed
EUROPEAN PHYSICAL JOURNAL PLUS
(2017)
Article
Physics, Multidisciplinary
Muhammad Aqeel, Anam Azam, Salman Ahmad
CHINESE JOURNAL OF PHYSICS
(2018)
Article
Mechanics
Abuzar Abid Siddiqui, Salman Ahmad, Muhammad Aqeel
Article
Automation & Control Systems
Muhammad Marwan, Salman Ahmad, Muhammad Aqeel, Muhammad Sabir
JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME
(2019)
Article
Physics, Multidisciplinary
Zainab Rana, Muhammad Aqeel, Javeria Ayub, Mansoor Shaukat
CHINESE JOURNAL OF PHYSICS
(2019)
Article
Computer Science, Artificial Intelligence
Muhammad Marwan, Memoona Mehboob, Salman Ahmad, Muhammad Aqeel
Article
Physics, Multidisciplinary
Muhammad Fiaz, Muhammad Aqeel, Salman Ahmad, Javeria Ayub
CHINESE JOURNAL OF PHYSICS
(2019)
Article
Nanoscience & Nanotechnology
Javeria Ayub, Muhammad Aqeel, Javeria Nawaz Abbasi, Danish Ali Sunny, Zainab Rana
Article
Computer Science, Artificial Intelligence
Muhammad Marwan, Salman Ahmad
Article
Mathematics, Interdisciplinary Applications
Muhammad Sabir, Muhammad Marwan, Salman Ahmad, Muhammad Fiaz, Farhan Khan
CHAOS SOLITONS & FRACTALS
(2020)
Article
Nanoscience & Nanotechnology
Muhammad Fiaz, Muhammad Aqeel
Article
Physics, Multidisciplinary
Muhammad Aqeel, Anam Azam, Javeria Ayub
Summary: The present study focuses on controlling the chaotic behavior of the geomagnetic Krause and Roberts system using state space linearization technique. A numerical comparison with linear and nonlinear feedback control techniques is presented to observe the effectiveness of state space linearization. It is observed that the proposed state space linearization controller can effectively control the large oscillations of the Krause and Roberts system compared to linear and nonlinear feedback controllers.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Ecology
Javaria Iqbal, Salman Ahmad, Muhammad Marwan, Ayesha Rafiq
Summary: This study considers a chaotic system involved in virus injection for cancer treatment, and designs adaptive and passive control techniques for the therapy. Both controllers, aided by a quadratic Lyapunov function, are able to achieve global stability of the cancer system, while the adaptive control technique shows better results.
JOURNAL OF BIOLOGICAL DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Muhammad Sabir, Salman Ahmad, Muhammad Marwan
Summary: This article investigates the dynamical behavior and stability of velocity vectors in a moving spacecraft by coupling a fuel tank with a gyrostat. Parametric study is conducted using Hopf bifurcation to find bifurcation parameter, and a controller is designed for global stability based on Lyapunov theory. Numerical simulations are performed to validate the analytical results.
