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Conjugate Gradient (CG) methods are widely used for solving large-scale nonlinear systems of equations arising in various real-life applications due to their efficiency in employing vector operations. However, the global convergence analysis of CG methods remains a significant challenge. In response, this study proposes scaled versions of CG parameters based on the renowned Barzilai-Borwein approach for solving convex-constrained monotone nonlinear equations. The proposed algorithms enforce a sufficient descent property independent of the accuracy of the line search procedure and ensure global convergence under appropriate assumptions. Numerical experiments demonstrate the efficiency of the proposed methods in solving large-scale nonlinear systems, including their applicability to accurately solving the inverse kinematic problem of a 3DOF robotic manipulator, where the objective is to minimize the error in achieving a desired trajectory configuration.

In this study, the chaotic behavior of a second-order circuit comprising a nonlinear resistor and Chua’s diode is investigated. This circuit, which includes a nonlinear capacitor and resistor among its components, is considered one of the simplest nonautonomous circuits. The research explores various oscillator characteristics, emphasizing their chaotic properties through bifurcations, Lyapunov exponents, periodicity, local Lyapunov region, and resonance. The system exhibits both stable equilibrium points and a chaotic attractor. Additionally, the second objective of this study is to develop a novel cryptographic technique by incorporating the designed circuit into the S-box method. The evaluation results suggest that this approach is suitable for secure cryptographic applications, providing insights into constructing a cryptosystem for images and text based on its complex behavior. Real-life data were analyzed using various statistical and performance criteria after applying the proposed methodology. These findings enhance the reliability of the cryptosystems. Moreover, The proposed methods are assessed using a range of statistical and performance metrics after testing the text and images. The cryptographic results are compared with existing techniques, reinforcing both the developed cryptosystem and the performance analysis of the chaotic circuit.

In this paper, a fractional-order model of a financial risk dynamical system is proposed and the complex behavior of such a system is presented. The basic dynamical behavior of this financial risk dynamic system, such as chaotic attractor, Lyapunov exponents, and bifurcation analysis, is investigated. We find that numerical results display periodic behavior and chaotic behavior of the system. The results of theoretical models and numerical simulation are helpful for better understanding of other similar nonlinear financial risk dynamic systems. Furthermore, the adaptive fuzzy control for the fractional-order financial risk chaotic system is investigated on the fractional Lyapunov stability criterion. Finally, numerical simulation is given to confirm the effectiveness of the proposed method.

Synchronization of the chaotic systems has attracted much attention in recent years due to its vital applications in secured communication systems. In this paper, an implementation and comparative analysis of two different control approaches for synchronization between two identical four-dimensional hyperchaotic systems is presented. The two control approaches are the Adaptive nonlinear controller and the linear optimal quadratic regulator LQR. To demonstrate the effectiveness of each controller, the numerical simulation is presented using Matlab/Simulink and the control law is derived. The performance of the proposed controllers is compared based on four factors; response time, squared error integration, energy applied from the controller, and cost function. To measure the robustness of the control approaches, the performance factors are compared when there is a change in system parameters and a variation in the initial conditions. Then the proposed synchronization methods are implemented on the FPGA platform to demonstrate the utilized resources on Field Programmable Gate Array (FPGA) hardware platform and the operation speed. Finally, to generalize the results of the comparison, the study is implemented for the synchronization of another secured communication system consisting of two identical three-dimensional chaotic. The experimental results show that the LQR method is more effective than the Adaptive controller based on the performance factors we propose. Moreover, the LQR is much simpler to implement on hardware and requires fewer resources on the FPGA.

In this paper, fractional calculus has proven to be invaluable in disease transmission dynamics and the creation of control systems, among other real-world problems. To investigate vaccine and treatment dynamics for disease control, this work focuses on Kawasaki illness and uses a unique fractional operator called the modified Atangana-Baleanu-Caputo derivative. The stability analysis, positivity, boundedness, existence, and uniqueness, are treated for the proposed model with novel fractional operators. Additionally, it investigates the effects of different parameters on the reproductive number. It verifies the existence and uniqueness of the solutions to the suggested model using Banach fixed point and the Leray-Schauder nonlinear alternative theorem. Employs Lyapunov functions to determine the model equilibria analysis global stability. The numerical simulation and results utilized the two-step Lagrange interpolation approach at various fractional order values. The results are contrasted with those obtained using the widely recognized ABC method and comparisons are also made to show the effects of the proposed method for the epidemic system. This model advances beyond existing Kawasaki disease models by incorporating fractional-order dynamics, which capture memory effects and long-range dependencies in biological systems, offering more accurate representations of disease progression. The inclusion of chaos stability control provides novel insights into managing complex, nonlinear behaviors, enhancing both theoretical understanding and potential clinical applications.

The main problem with electricity supply on densely populated islands is reliable, low-carbon, and sustainable electricity. The availability of potential energy needs in-depth observation to ensure that the system can be built sustainably. This paper examines the integration of PV systems and diesel power systems on Karimunjawa Island to meet the need for reliable systems from economic, ecological, and technological aspects. Using the DigSilent Power Factory program to obtain the system response interference and penetration of the Photovoltaic (PV) system. Furthermore, this paper also tests short circuit analysis and economic feasibility analysis while validating the Levelized Cost of Electricity (LCOE) and Electric Production Cost (EPC) approaches. The results show that the availability of irradiation can handle the electricity needs on Karimunjawa Island. In addition, it proposes the designed requirements for an integrated PV power system and Diesel Power Plant (DPP) system. The research has also captured the synergistic profile of PV and DPP working coordination within 24 h.

Alzheimer’s disease, a prevalent neurological condition causing dementia, is characterized by hyperphosphorylated tau protein intracellular neurofibrillary tangles and amyloid beta-peptide extracellular plaques. Currently, medication cannot cure, stop, or slow its progression. This paper presents a novel epidemiological model for Alzheimer’s disease, considering both integer and fractional order operators to characterize the temporal dynamics of key cell populations. The analysis reveals a single solution to a proposed system with a positively invariant region. The Banach fixed-point theorem and Krasnoselskii type are used to investigate the uniqueness of the model. Local and global stability characteristics are analyzed, and the disease impact on compartments and community-wide transmission rates is evaluated. The study conducts a sensitivity analysis of parameters using chaos analysis. A linear feedback control strategy is employed to manage chaotic situations by directing system dynamics towards equilibrium points. A numerical scheme utilizing the Newton polynomial interpolation method is presented in the study, along with its solutions and MATLAB simulations that demonstrate the behavior of the model. With different results for varying values, the fractal fractional order model performs better in medical interventions than the conventional integer order model, pointing to new possibilities for advancement. The study improves our understanding of the progression and recurrence of neurological diseases, which will benefit in disease spread investigation and the development of control techniques.

This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points’ stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model’s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system’s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

The farming of animals is one of the largest industries, with animal food products, milk, and dairy being crucial components of the global economy. However, zoonotic bacterial diseases, including brucellosis, pose significant risks to human health. The goal of this research is to develop a mathematical model to understand the spread of brucellosis in cattle populations, utilizing the Caputo-Fabrizio operator to control the disease’s incidence rate. The existence and uniqueness of the model’s solution are ensured through the Lipschitz conditions, the contraction mapping theorem, and the application of the kernel properties of the Caputo-Fabrizio operator. Sensitivity analysis is conducted to assess the impact of various factors on the disease’s progression. This study performs a realistic stability analysis of both global and local stability at the disease-free and the endemic equilibrium point which give a more accurate understanding of the dynamism and behavior of the system. Stability analysis is performed using Picard stability in Banach spaces, and Lagrange’s interpolation formula is employed to obtain initial approximations for successive fractional orders. The findings of this study demonstrate that fractional orders, along with memory effects, play a crucial role in describing the transmission dynamics of brucellosis. Sensitivity analysis helps identify the parameters most critical to the infection rate, providing essential data for potential control measures. The results highlight the applicability of the Caputo-Fabrizio operator in modeling the transmission of infectious diseases like brucellosis and offer a strong foundation for controlling disease spread within communities.