Article
Mathematics, Interdisciplinary Applications
Abdullah Gokyildirim
Summary: Interest in fractional calculus and its applications has been increasing, and fractional-order analysis has the potential to enhance chaotic systems. This study presents the implementation of a lower-order fractional electronic circuit for the Sprott K system, which is pioneering in achieving a fractional-order parameter of approximately 0.8. Various numerical analyses are conducted to examine the dynamic characteristics and complexity of the system, and the voltage outputs from the oscilloscope show good agreement with the numerical analysis and simulations.
FRACTAL AND FRACTIONAL
(2023)
Article
Acoustics
Abdullah Gokyildirim, Haris Calgan, Metin Demirtas
Summary: In this study, the chaotic behavior of a 4D memristive Chen system is investigated by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Two different fractional orders are determined where the system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the system on the equilibrium points.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Materials Science, Multidisciplinary
Mati Ur Rahman, M. A. El-Shorbagy, Hussam Alrabaiah, Dumitru Baleanu, Manuel De la Sen
Summary: This study investigates a modified conservative 4D chaotic system using both integer and non-integer order derivatives. Various aspects of the model are explored, and hidden and fixed point chaotic attractors are found for certain fractional order values.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohammed Almuzaini, Abdullah Alzahrani
Summary: The study proposes a new chaotic system with a cubic non-linear term and investigates various characteristics of the system such as equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents. The electronic circuit and signal flow graph are implemented to demonstrate the applicability of the chaotic system. The study also focuses on achieving complete synchronization between two similar novel chaotic systems and applying it in secure communication using Lyapunov stability theorem.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Ahmed Sadeq Hunaish, Fadhil Rahma Tahir
Summary: The dynamics of a nonlinear drilling system with a two Degree of Freedom (DoF) drilling string actuated by an AC drive system are investigated in this paper. An indirect field oriented controlled induction motor (IFOCIM) is used as the controller for the AC drive system. The derived drilling system model consists of eleven nonlinear first order differential equations. Mathematical and numerical analyses are used to find the equilibrium points of the drilling system model. The nonlinear dynamics of the induction motor drive-based drilling system are investigated numerically, showing various types of oscillations such as periodic, chaotic, and fixed point attractors, as well as coexistence attractors.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Gayathri Vivekanandhan, Hayder Natiq, Aboozar Ghaffari, Atiyeh Bayani, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper presents a chaotic jerk oscillator with a heart-shaped attractor and the coexistence of chaotic and periodic attractors. The analysis of bifurcation diagram, Lyapunov exponent, and basin of attraction confirms the chaotic and periodic properties of the oscillator.
Article
Engineering, Electrical & Electronic
Abdullah Gokyildirim, Ugur Erkin Kocamaz, Yilmaz Uyaroglu, Haris Calgan
Summary: Data security has gained importance, and cryptology is becoming popular. A new five-term 3D chaotic flow with cubic nonlinearity has been proposed for more difficult-to-decrypt systems. The research analyzed the dynamic characteristics of the introduced system and demonstrated its applicability through numerical analyses and circuit implementation. A secure communication method using the chaotic masking method was also designed and implemented to validate the system.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2023)
Article
Mathematics
Tareq Saeed, Kamel Djeddi, Juan L. G. Guirao, Hamed H. Alsulami, Mohammed Sh Alhodaly
Summary: In this paper, a continuous state cancer system and various numerical results are presented. Discretization methods, such as the Euler method, Taylor series expansion method, and Runge-Kutta method, are introduced and applied to the cancer system. The stability of fixed points in the discrete cancer system is studied using a modified version of Marotto's theorem, and it is proven that the discrete cancer system exhibits chaos. Numerical simulations, including Lyapunov exponents and bifurcation diagrams, are also presented.
Article
Mathematics, Applied
D. E. Onder, A. A. S. Kalaee, D. O. Winge, A. Wacker
Summary: The ignition of Quantum Cascade Lasers can occur from a state of oscillating field domains, leading to complex oscillation scenarios. Analysis of numerical findings for devices operating at terahertz frequencies show they can exhibit chaotic behavior with positive Lyapunov exponents even without periodic driving. This highlights the importance of considering chaotic evolution in the design of these devices.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Guy Morgand Djeufa Dagoumguei, Samuel Tagne, J. S. Armand Eyebe Fouda, Wolfram Koepf
Summary: This paper presents a real-time monitoring system for system dynamics using the PIC micro-controller based PLSE algorithm. The algorithm is optimized for low-end processors and implemented on the PIC16F18446. The tool efficiently monitors the behavior of dynamical systems by comparing PLSE values with phase portraits and previous results.
Article
Mathematics, Interdisciplinary Applications
Alexander P. Kuznetsov, Yuliya Sedova, Nataliya Stankevich
Summary: The interaction between a system with quasi-periodic autonomous dynamics and a chaotic Rössler system is studied. The coupling growth leads to the emergence of two-frequency and three-frequency quasi-periodicity, periodicity, and oscillation death in sequence. The system exhibits doubling bifurcations of three-frequency tori with small coupling strength. A chaotic regime with two additional zero Lyapunov exponents in the spectrum is discovered. Two-parameter Lyapunov exponent analysis and bifurcation analysis are conducted, and a new bifurcation scenario from oscillation death to quasi-periodicity in coupled systems is described.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Hardware & Architecture
Belqassim Bouteghrine, Camel Tanougast, Said Sadoudi
Summary: This paper introduces a novel multidimensional chaotic system with multiple parameters and nonlinear terms, and proposes a two-phase algorithm for investigating chaotic behavior. By constructing multiple chaotic maps to generate random keys for communication security, the scheme demonstrates feasibility in resource-constrained devices and IoT applications.
JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS
(2021)
Article
Mathematics
Jiri Petrzela
Summary: This paper presents recent findings on the Clapp oscillator circuit, exploring parameter regions that lead to chaotic or hyperchaotic dynamics, and conducting in-depth analysis through numerical tools. The structural stability of strange attractors observed numerically was proven via a practical experiment.
Article
Mathematics, Interdisciplinary Applications
Lone Seth Jahanzaib, Pushali Trikha, Rajaa T. Matoog, Shabbir Muhammad, Ahmed Al-Ghamdi, Mahmoud Higazy
Summary: This paper investigates a fractional-order chaotic system with sine non-linearities, analyzing its dynamics using Lyapunov spectrum and bifurcation analysis. Through nonlinear control and adaptive sliding mode technique, synchronization was achieved among multiple master and slave systems, considering uncertainties and disturbances. The successful synchronization was demonstrated to have applications in secure communication.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
M. D. Vijayakumar, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Iqtadar Hussain
Summary: The paper introduces a quadratic hyperjerk system that can generate chaotic attractors and investigates its dynamical behaviors through Lyapunov exponents and bifurcation diagrams. The study reveals multistability of the system, exploring bistability caused by hidden attractors, as well as the complexity of the system's attractors using sample entropy. Additionally, impulsive control is used to stabilize one of the hyperjerk system equilibrium points, making all real initial conditions become equilibrium points of the basin of attraction.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Engineering, Electrical & Electronic
Selcuk Emiroglu, Akif Akgul, Yusuf Adiyaman, Talha Enes Gumus, Yilmaz Uyaroglu, Mehmet Ali Yalcin
Summary: A new 4D hyperchaotic system is developed in this paper by adding a state variable and controller to achieve synchronization and stability, with experimental validation confirming the accuracy of numerical simulations.
Article
Mathematics, Interdisciplinary Applications
Yousuf Islam, Chunbiao Li, Yicheng Jiang, Xu Ma, Akif Akgul
Summary: This paper studies a three-dimensional chaotic system with a line equilibrium, in which a single nonbifurcation parameter is used to control the amplitude and frequency. A variety of chaotic signals can be modified using the amplitude-frequency control switch. The theoretical analysis is further verified through circuit simulation based on Multisim. Finally, a method for encrypting color images is tested and its performance is evaluated, showing a promising application prospect of the novel chaotic oscillation in image encryption.
Article
Engineering, Biomedical
Kasim Serbest
Summary: Obesity is a global health issue and its prevalence is increasing. Previous studies focused on the biomechanical effects of weight gain on knee and hip joints, but failed to compare the differences between male and female weight gain. This study found that weight gain in the abdominal region (specific to men) increases ankle and knee joint moments more than weight gain in the gluteal-femoral region (specific to women). In obese scenarios for both genders, ankle and knee joint moments increase while hip joint moment decreases.
BIOMEDICAL ENGINEERING-BIOMEDIZINISCHE TECHNIK
(2022)
Article
Mathematics, Interdisciplinary Applications
Fahrettin Horasan, Muhammed Ali Pala, Ali Durdu, Akif Akgul, Omer Faruk Akmese, Mustafa Zahid Yildiz
Summary: Watermarking is a commonly used technique to protect data's authenticity and security. This article introduces the application of a watermarking method based on chaos-based random number generators in biomedical data to solve problems such as visual attack and identity theft.
Article
Computer Science, Hardware & Architecture
Akif Akgul, Yusuf Adiyaman, Abdullah Gokyildirim, Burak Aricioglu, Muhammed Ali Pala, Murat Erhan Cimen
Summary: This paper presents the dynamical analysis and fractional-order circuit implementation of the Rucklidge chaotic system. The component values required for the fractional-order system are calculated, and the feasibility of the attractor is examined using an electronic circuit with a fractional-order module. The experimental results show that the chaotic state of the system disappears as the fractional degree decreases.
JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS
(2023)
Article
Engineering, Mechanical
Hamid Asadi Dereshgi, Kasim Serbest
Summary: This study investigated the effects of dumbbell weight on shoulder biomechanics during dumbbell fly movements. Through simulation and finite element modeling, it was found that increasing the weight of the dumbbell increased joint moment and muscle force, but more noticeably increased stress in the deltoid muscle.
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Balamurali Ramakrishnan, Murat Erhan Cimen, Akif Akgul, Chunbiao Li, Karthikeyan Rajagopal, Hakan Kor
Summary: This paper explores a linear resistive capacitive inductive shunted model of a Josephson junction with a topologically nontrivial behavior. A fractional-order flux-controlled memristor is introduced to effectively model the feedback flux effects across the Josephson junction. The proposed Josephson junction oscillator exhibits both stable and unstable regions of oscillations for different choices of equilibrium points and fractional order, with regions of coexisting attractors. Synchronization of the oscillator is achieved using fuzzy sliding mode control, with estimation of the chattering amplitude through fuzzy logic to minimize error.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Xingrong Chen, Min Zou, Akif Akgul
Summary: In this study, a generalized system is proposed to investigate the hidden chaotic attractors and their generating mechanism in the Vijayakumar system. Hopf bifurcations are considered using the first and second Lyapunov coefficients, and the existence of periodic orbits is theoretically proven. The findings of this study provide valuable insights into the relationship between the global complex dynamical behaviors of chaotic systems and the local stability of equilibria.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Optics
Omer Faruk Boyraz, Emre Guleryuz, Akif Akgul, Mustafa Zahid Yildiz, Harun Emre Kiran, Jawad Ahmad
Summary: Hand vein images are important for identification systems, especially dorsal hand vein images due to their reliability and contactless procedure. A new identification application is proposed in this article, using chaos-based security mechanism and improved SURF method, which selects vein segments as features and eliminates mismatching points to increase accuracy.
Article
Computer Science, Information Systems
Asad Ullah, Awais Aziz Shah, Jan Sher Khan, Mazhar Sajjad, Wadii Boulila, Akif Akgul, Junaid Masood, Fuad A. Ghaleb, Syed Aziz Shah, Jawad Ahmad
Summary: With the increasing use of Internet multimedia applications, ensuring the security of digital images has become crucial. This study proposes a lightweight nonlinear mechanism based on chaos theory for encrypting digital images. Through various security parameter tests, the proposed scheme has been proven to be highly secure and effective.
SECURITY AND COMMUNICATION NETWORKS
(2022)
Article
Engineering, Multidisciplinary
Zhinan Li, Chunbiao Li, Akif Akgul, Lvqing Bi, Yicheng Jiang
Summary: Chaotic neuronal oscillation is activated in the Rossler system when a locally active memristor is introduced. The memristive Rossler system has two independent parameters that provide local amplitude control, one of which can adjust the amplitude and frequency of variables in a specific intermittent mode. Different neuronal firing modes are modified by the system parameter. The coexistence of periodic oscillation and chaos is also captured along with a basin of attraction. Experimental verification using STM32-based experiment supports the numerical and theoretical results.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Computer Science, Artificial Intelligence
Kasim Serbest, Murat Tolga Ozkan, Murat Cilli
Summary: Joint torques are important in studying human movements. Indirect methods, such as mathematical techniques and artificial neural networks, are commonly used to estimate joint torques. In this study, a four-layer neural network was trained to estimate joint torques using input data from angular displacements, segment heights, and segment mass.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
Isidore Komofor Ngongiah, Ramakrishnan Balamurali, Gaetan Fautso Kuiate, Akif Akgul, Bonaventure Nana
Summary: The article investigates single and array of mechanical arms driven by Josephson junction (JJ) circuits and their applications in mimicking the locomotion of myriapods. The stability analysis of a single mechanical arm driven by a JJ circuit reveals two equilibrium points and a switch of their stability for specific values of the stimulation current. Numerical simulations confirm the proposed electromechanical system's ability to mimic the motion of myriapods and overcome the difficulties of coupling many JJ circuits or other neuron circuit models. The progressive excitation of the array of mechanical arms in the electromechanical system, as demonstrated by numerical simulations, resembles the straightforward motion of myriapods.
Article
Mathematics, Applied
Sridevi Sriram, Karthikeyan Rajagopal, Anitha Karthikeyan, Akif Akgul
Summary: The network connectivities are crucial for exhibiting diverse collective dynamics in complex systems. Hindmarsh-Rose neurons connected by electromagnetic interactions are used to demonstrate different dynamical states and transitions. Specifically, the dynamical behaviors of the system are explored under regular, small-world, and random network connectivities. The results show that increasing coupling intensity leads to a transition from desynchronization to traveling wave state for all considered network interactions. Furthermore, the investigation is extended to a three-layer multiplex network where synchronization is achieved in all layers with increasing coupling intensity, eventually reaching a rest state at high coupling strength.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Mohammed Mansour, Kasim Serbest, Mustafa Kutlu, Murat Cilli
Summary: The aim of this study is to estimate the joint moments of the ankle, knee, and hip joints during walking. Various algorithms including decision tree, linear regression, support vector machine, random forest, and three deep learning algorithms were examined to estimate the joint moments. LSTM algorithm was found to be the most accurate in predicting knee, hip, and ankle joint moments. The prediction of joint moments is crucial in designing biomechanical systems and has potential applications in real-time prosthesis/orthosis controllers.
MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING
(2023)
