Article
Mathematics, Interdisciplinary Applications
A. Dlamini, Emile F. Doungmo Goufo, M. Khumalo
Summary: The application of fractal-fractional derivatives and integrals has opened doors to ongoing research in different fields. This paper aims to extend the existing work by applying these operators to a modified STF flow and studying its dynamic behavior using numerical methods and simulations.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Physics, Multidisciplinary
Chenhua Li, Zhouchao Wei, Wei Zhang
Summary: A new unified stretch-twist-fold flow is proposed, exploring conditions for zero-Hopf bifurcation and deriving a periodic solution from the zero-Hopf equilibrium using the first-order averaging theorem. For large enough parameter alpha, it is concluded that the periodic orbit of the USTF flow exists but is unstable. Experimental results show good agreement between circuit design, computer simulations, and experimental observations.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Kang-jia Wang, Guo-dong Wang
Summary: This study proposes a modified equal width equation with fractal derivatives to study the motion morphology of ion-acoustic waves in plasma. By utilizing the fractal variational formulation and He's variational method, combined with a two-scale transform, the periodic and solitary wave solutions of the equation are successfully found, opening up new perspectives for the study of traveling wave theory in fractal space.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics
Guanggang Liu, Yong Li, Xue Yang
Summary: In this paper, the rotating periodic solutions of a Hamiltonian system with a twist condition are considered. The system has a form x(t + T) = Qx(t), where x∈R2N and Q is a symplectic orthogonal matrix. The existence and multiplicity of nontrivial rotating periodic solutions are established by combining a finite dimensional reduction method, Morse theory, and minimax principle.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Adil Jhangeer, Amjad Hussain, M. Junaid-U-Rehman, Dumitru Baleanu, Muhammad Bilal Riaz
Summary: This paper investigates the nonlinear modified Gardner equation through Lie group analysis, converting partial differential equations into ordinary differential equations using similarity reduction method and constructing exact solutions using power series technique. The Galilean transformation is used to transform the model into a planar dynamical system, and various types of phase portraits are plotted with sensitivity analysis and the application of extrinsic periodic power to study the influence on the model's behavior.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Ning Han, Zhixin Li
Summary: This study investigates the oscillating periodic solutions of a classical pendulum system with an irrational and fractional nonlinear restoring force under small perturbations of viscous damping and harmonic excitation. A simplified approximate system is introduced to precisely describe the local dynamics of small-angle oscillations, successfully retaining non-smooth characteristics and reflecting the complex restoring force features. The study extends the application range of the simplified system compared to polynomial systems, and uses numerical simulations to verify theoretical analysis and demonstrate periodic motions.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Chemistry, Physical
Xuwen Deng, Songxiao Hui, Wenjun Ye, Rui Liu, Liang Huang
Summary: In this study, the hot deformation behavior of Ti-6Al-4V profile prepared by hot extrusion was investigated. The coupled thermo-mechanical model of hot twist-stretch straightening was established and the effects of process parameters on the bending deflection and torsion angle were systematically studied and optimized. The results showed that the straightening accuracy can meet the requirements by using the optimized process parameters.
Article
Acoustics
Hui Yang, Rui Guo
Summary: The modified nonlinear Schrodinger (MNLS) equation is used to describe the propagation of femtosecond pulses and modulated Alfven waves in different physical systems. By constructing nonlocal type Darboux transformations (DTs), several new solutions are derived, including bright and dark solitons, periodic solutions, breathers, and rogue wave solutions. The dynamic behaviors of these solutions are discussed through graphic simulations.
Article
Mathematics, Applied
Yanling Shi, Junxiang Xu
Summary: This paper discusses the solutions of the two-dimensional modified Boussinesq equation under periodic boundary conditions, proving the existence of a specific class of solutions and providing a mathematical proof for it.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2021)
Article
Physics, Multidisciplinary
Min Xue, Zhigang Li, Yuchen Zhu
Summary: By using the reciprocal transformation between the modified short pulse (mSP) equation and the sine-Gordon (sG) equation, periodic solutions of the mSP equation are constructed and further used to recover solitary wave solutions and novel standing wave solutions. The obtained solutions include one-phase and two-phase periodic solutions, as well as one-cuspon, two-cuspon, and one-breather solutions.
PRAMANA-JOURNAL OF PHYSICS
(2023)
Article
Mathematics, Applied
Yongjian Liu, Biyu Chen, Xiezhen Huang, Li Ye, Zhouchao Wei
Summary: This paper focuses on the qualitative geometric analysis of traveling wave solutions of the MEW-Burgers wave equation. It transforms the MEW-Burgers equation into an equivalent planar dynamical system using the traveling wave transformation. The global structure of the planar system is presented, and solitary waves, kink waves, and periodic waves are found. The paper then studies the Jacobi stability of the planar system based on KCC theory, analyzing the dynamical behavior near equilibrium points and comparing Lyapunov stability and Jacobi stability. It also transforms the planar system with periodic disturbance into a six-dimensional nonlinear system and numerically simulates the periodic, quasi-periodic, and chaotic dynamical behaviors of the system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Physics, Multidisciplinary
Yuan Shen, Bo Tian, Dan-Yu Yang, Tian-Yu Zhou
Summary: This paper examines a hybrid relativistic and modified Toda lattice-type system and provides an equivalent form using certain transformations. Based on the Lax pair of the equivalent form, an N-fold Darboux matrix is constructed and the N-fold Darboux transformation is derived, resulting in some analytic solutions.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics
Rong Chen, Shihang Pan, Baoshuai Zhang
Summary: In this paper, the behavior of a solution beyond wave breaking for a modified periodic Coupled Camassa-Holm system is studied. By introducing new independent and dependent variables to resolve singularities, the evolution system is rewritten as a closed semilinear system. The local existence of the semilinear system is obtained as fixed points of a contractive transformation, providing a global conservative solution and repairing some gaps in previous work.
ELECTRONIC RESEARCH ARCHIVE
(2021)
Article
Computer Science, Interdisciplinary Applications
Lijun Pei, Fanxin Wu
Summary: This paper investigates the periodic oscillations and dynamics of the state-dependent AIMD/RED congestion control system, and presents approximate analytical expressions of periodic solutions using a semi-analytical method. The study reveals harmful phenomena such as coexistence of chaos with periodic solutions, chaos routes, and windows to chaos, emphasizing the need to avoid these complex dynamical behaviors. The obtained results can aid researchers in understanding network congestion control mechanisms and improving network stability and performance.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Yuika Kajihara, Eiko Kin, Mitsuru Shibayama
Summary: Periodic solutions of the planar N-body problem determine braids through the trajectory of N bodies. Braid types can be used to classify periodic solutions. According to the Nielsen-Thurston classification of surface automorphisms, braids fall into three types: periodic, reducible and pseudo-Anosov. To a braid of pseudo-Anosov type, there is an associated stretch factor greater than 1, and this is a conjugacy invariant of braids. In 2006, the third author discovered a family of multiple choreographic solutions of the planar 2n-body problem. We prove that braids obtained from the solutions in the family are of pseudo-Anosov type, and their stretch factors are expressed in metallic ratios. New numerical periodic solutions of the planar 2n-body problem are also provided.
TOPOLOGY AND ITS APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
Muhammad Aqeel, Anam Azam, Salman Ahmad
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.
