Search Results (28)

Cascade reservoir optimization faces significant challenges due to multi-dimensional, non-convex, and nonlinear characteristics with coupled constraints. As reservoir numbers increase, computational complexity escalates dramatically, limiting conventional optimization methods’ effectiveness. This paper proposes HHONMPA, a hybrid algorithm combining Harris Hawks Optimization (HHO) with Marine Predators Algorithm (MPA). The method uses SPM chaotic mapping for population initialization to enhance diversity and integrates both algorithms’ predatory behaviors. During exploration, it employs Brownian motion and improved Lévy flight strategies for global search, while exploitation uses enhanced HHO for local optimization. A novel Dual-Period Oscillation Attenuation Strategy dynamically adjusts parameters to balance exploration-exploitation. Performance validation using CEC2017 benchmark functions shows HHONMPA significantly outperforms the original HHO and MPA in solution accuracy and convergence speed, confirmed through statistical testing. Engineering validation applies the algorithm to the Lower Jinsha River—Three Gorges four-reservoir system, conducting experiments across various hydrological scenarios. Results demonstrate substantial improvements in search accuracy and convergence efficiency compared to existing methods. HHONMPA effectively addresses large-scale cascade reservoir optimization challenges, offering promising prospects for water resource management and hydropower scheduling applications. Full article

The study of economic maps has consistently attracted researchers due to their rich dynamics and practical relevance. A deeper understanding of these systems enables the development of more effective control strategies. In this work, we examine the influence of the fractional order $\upsilon$ with the Caputo fractional difference on an economic market map. The primary contribution is the comprehensive analysis of how both commensurate and incommensurate fractional orders affect the stability and complexity of the map. Numerical investigations, including phase portraits, largest Lyapunov exponents, and bifurcation analysis, reveal that the system undergoes a cascade of period-doubling bifurcations before transitioning into chaos. To further characterize the dynamics, complexity is evaluated using the 0–1 test and $C_0$ complexity, both confirming chaotic behavior. Furthermore, two-dimensional control schemes are introduced and theoretically validated to both stabilize the chaotic economic market map and achieve synchronization with a combined response map. The theoretical and numerical results are validated through MATLAB 2016 simulations. Full article

In the era of digital communication, securing sensitive information against increasingly sophisticated cyber threats remains a critical challenge. Chaos synchronization, while promising for secure communication and control systems, faces key limitations, including high sensitivity to parameter mismatches and initial conditions, vulnerability to noise, and difficulties in maintaining stability for high-dimensional systems. This paper presents a novel secure communication system based on multi-level synchronization of three distinct chaotic systems: the Bhalekar–Gejji (BG) system, the Chen system, and a 3D chaotic oscillator. Utilizing the nonlinear active control (NAC) method, we achieve robust synchronization between master and slave systems, ensuring the stability of the error dynamics through Lyapunov theory. The proposed triple-cascade masking technique enhances security by sequentially embedding the information signal within the chaotic outputs of these systems, making decryption highly challenging without knowledge of all three systems. Numerical simulations and Simulink implementations validate the effectiveness of the synchronization and the secure communication scheme. The results demonstrate that the transmitted signal becomes unpredictable and resistant to attacks, significantly improving the security of chaos-based communication. This approach offers a promising framework for applications requiring high levels of data protection, with potential extensions to image encryption and other multimedia security domains. Full article

This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form approach and bifurcation theory to explore codimension-one and two bifurcation behaviors for this model. The primary conclusions are substantiated by a combination of rigorous theoretical analysis and meticulous computational simulations. Additionally, utilizing fractal basin boundaries, periodicity variations, and Lyapunov exponent distributions within two-parameter spaces, we observe a mode-locking structure akin to Arnold tongues. These periods are arranged in a Farey tree sequence and embedded within quasi-periodic/chaotic regions. These findings enhance comprehension of bifurcation cascade emergence and structural patterns in diverse biological systems with discrete dynamics. Full article

Increasing environmental variability and operational complexity in reservoir systems necessitate advanced optimization frameworks for flood control. This study proposes the ε-constrained Improved Zebra Optimization Algorithm (ε-IZOA), a novel metaheuristic algorithm integrating an enhanced Zebra Optimization Algorithm (ZOA) with adaptive ε-constraint handling, to address multi-reservoir flood control optimization. Three strategic modifications advance the standard ZOA: (1) Bernoulli chaotic mapping for diversified population initialization; (2) adaptive weight balancing for exploration-exploitation trade-off mitigation; and (3) golden sinusoidal vectorization for global search refinement, collectively forming the Improved ZOA (IZOA). The ε-IZOA synergizes IZOA with ε-dominance criteria to dynamically resolve constrained optimization conflicts. Applied to the Yellow River Basin’s five-reservoir cascade, ε-IZOA achieves a 52.97% peak shaving rate at Huayuankou Station, reducing the maximum discharge to 18,745.02 m³/s—a performance surpassing benchmark methods. The algorithm’s success stems from its bio-inspired hybrid architecture, which embeds swarm intelligence principles into nonlinear constraint management. This work establishes ε-IZOA as a computationally robust tool for large-scale reservoir optimization, with implications for mitigating flood risks in climate-sensitive basins. Future research should prioritize its integration with real-time hydrological forecasting systems. Full article

In recent years, chaos-based secure communication systems have garnered significant attention for their unique attributes, including sensitivity to initial conditions and periodic orbit density. However, existing systems face challenges in balancing encryption strength with practical implementation, especially for multiple levels. This paper addresses this gap by introducing a novel N-level cascaded chaotic-based secure communication system for voice encryption, leveraging the four-dimensional unified hyperchaotic system. Performance evaluation is conducted using various security metrics, including Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR), Percent Residual Deviation (PRD), and correlation coefficient, as well as Field-Programmable Gate Array (FPGA) resource metrics. A new Value-Based Performance Metrics (VBPM) framework is also introduced, focusing on both security and efficiency. Simulation results reveal that the system achieves optimal performance at N = 4 levels, demonstrating significant improvements in both security and FPGA resource utilization compared to existing approaches. This research offers a scalable and cost-efficient solution for secure communication systems, with broader implications for real-time encryption in practical applications. Full article

Based on the chaotic polarization system of optically injected cascaded vertical-cavity surface-emitting lasers (VCSELs), we propose a novel implementation scheme for high-speed optical chaotic data selection logic operations. Under the condition where the slave VCSEL (S-VCSEL) outputs a chaotic laser signal, we calculate the range of the applied electric field and the optical injection amplitude. We also investigate the evolution of the correlation characteristics between the polarized light output from the periodic poled LiNbO3 (PPLN) and the S-VCSEL as a function of the optical injection amplitude under different applied electric fields. Furthermore, we analyze the polarization bistability of the polarized light from the PPLN and S-VCSEL. Based on these results, we modulate the optical injection amplitude as the logic input and the applied electric field as the control logic signal. Using a mean comparison mechanism, we demodulate the polarized light from the PPLN and S-VCSEL to obtain two identical logic outputs, achieving optical chaotic data selection logic operations with an operation speed of approximately 114 Gb/s. Finally, we investigate the influence of noise on the logic outputs and find that both logic outputs do not show any error symbols under the noise strength as high as 180 dBw. The anti-noise performance of logic output O₁ is superior to that of optical chaotic logic output O₂. For noise strengths up to 185 dBw, error symbols in O₂ can be detected and corrected by comparison with O₁. Full article

An important issue in interconnected microgrids (MGs) is the realization of balance between the generation side and the demand side. Imbalanced generation and load demands lead to security, power quality, and reliability issues. The load frequency control (LFC) is accountable for regulating MG frequency against generation/load disturbances. This paper proposed an optimized fractional order (FO) LFC scheme with cascaded outer and inner control loops. The proposed controller is based on a cascaded one plus tilt derivative (1+TD) in the outer loop and an FO tilt integrator-derivative with a filter (FOTIDF) in the inner loop, forming the cascaded (1+TD/FOTIDF) controller. The proposed 1+TD/FOTIDF achieves better disturbance rejection compared with traditional LFC methods. The proposed 1+TD/FOTIDF scheme is optimally designed using a modified version of the liver cancer optimization algorithm (MLCA). In this paper, a new modified liver cancer optimization algorithm (MLCA) is proposed to overcome the shortcomings of the standard Liver cancer optimization algorithm (LCA), which contains the early convergence to local optima and the debility of its exploration process. The proposed MLCA is based on three improvement mechanisms, including chaotic mutation (CM), quasi-oppositional based learning (QOBL), and the fitness distance balance (FDB). The proposed MLCA method simultaneously adjusts and selects the best 1+TD/FOTIDF parameters to achieve the best control performance of MGs. Obtained results are compared to other designed FOTID, TI/FOTID, and TD/FOTID controllers. Moreover, the contribution of electric vehicles and the high penetration of renewables are considered with power system parameter uncertainty to test the stability of the proposed 1+TD/FOTIDF LFC technique. The obtained results under different possible load/generation disturbance scenarios confirm a superior response and improved performance of the proposed 1+TD/FOTIDF and the proposed MLCA-based optimized LFC controller. Full article

In this paper, a new physical layer authenticated encryption (PLAE) scheme based on the multi-parameter fractional Fourier transform–Orthogonal frequency division multiplexing (MP-FrFT-OFDM) is suggested for secure image transmission over the IoT network. In addition, a new robust multi-cascaded chaotic modular fractional sine map (MCC-MF sine map) is designed and analyzed. Also, a new dynamic chaotic biometric signature (DCBS) generator based on combining the biometric signature and the proposed MCC-MF sine map random chaotic sequence output is also designed. The final output of the proposed DCBS generator is used as a dynamic secret key for the MPFrFT OFDM system in which the encryption process is applied in the frequency domain. The proposed DCBS secret key generator generates a very large key space of $2^{2200}$. The proposed DCBS secret keys generator can achieve the confidentiality and authentication properties. Statistical analysis, differential analysis and a key sensitivity test are performed to estimate the security strengths of the proposed DCBS-MP-FrFT-OFDM cryptosystem over the IoT network. The experimental results show that the proposed DCBS-MP-FrFT-OFDM cryptosystem is robust against common signal processing attacks and provides a high security level for image encryption application. Full article

In this work, an analytical and numerical analysis of the transition to chaos in five nonlinear systems of ordinary and partial differential equations, which are models of autocatalytic chemical processes and interacting populations, is carried out. It is shown analytically and numerically that in all considered systems of equations, further complication of the dynamics of solutions and the transition to chemical and biological turbulence is carried out in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic and homoclinic cascades of bifurcations of stable limit cycles. In this case, irregular (chaotic) attractors in all cases are exclusively singular attractors in the sense of the FShM theory. The obtained results once again indicate the wide applicability of the universal bifurcation FShM theory for describing laminar–turbulent transitions to chaotic dynamics in complex nonlinear systems of differential equations and that chaos in the system can be confirmed only by detection of some main cycles or tori in accordance with the universal bifurcation diagram presented in the article. Full article

As a kind of dynamical system with a particular nonlinear structure, a multi-time scale nonlinear system is one of the essential directions of the current development of nonlinear dynamics theory. Multi-time scale nonlinear systems in practical applications are often complex forms of coupling of high-dimensional and high codimension characteristics, leading to various complex bursting oscillation behaviors and bifurcation characteristics in the system. For exploring the complex bursting dynamics caused by high codimension bifurcation, this paper considers the normal form of the vector field with triple zero bifurcation. Two kinds of codimension-2 bifurcation that may lead to complex bursting oscillations are discussed in the two-parameter plane. Based on the fast–slow analysis method, by introducing the slow variable $W=Asin\left(\omega t\right)$, the evolution process of the motion trajectory of the system changing with W was investigated, and the dynamical mechanism of several types of bursting oscillations was revealed. Finally, by varying the frequency of the slow variable, a class of chaotic bursting phenomena caused by the period-doubling cascade is deduced. Developing related work has played a positive role in deeply understanding the nature of various complex bursting phenomena and strengthening the application of basic disciplines such as mechanics and mathematics in engineering practice. Full article

Multi-area power systems (MAPSs) are highly complex non-linear systems facing a fundamental issue in real-world engineering problems called frequency stability problems (FSP). This paper develops an enhanced slime mold optimization algorithm (ESMOA) to optimize the tuning parameters for a cascaded proportional derivative-proportional integral (PD-PI) controller. The novel ESMOA proposal includes a new system that combines basic SMO, chaotic dynamics, and an elite group. The motion update incorporates the chaotic technique, and the exploitation procedure is enhanced by searching for a select group rather than merely the best solution overall. The proposed cascaded PD-PI controller based on the ESMOA is employed for solving the FSP in MAPSs with two area non-reheat thermal systems to keep the balance between the electrical power load and the generation and provide power system security, reliability, and quality. The proposed cascaded PD-PI controller based on the ESMOA is evaluated using time domain simulation to minimize the integral time-multiplied absolute error (ITAE). It is evaluated in four different test situations with various sets of perturbations. For tuning the cascaded PD-PI controller, the proposed ESMOA is compared to the golden search optimizer (GSO) and circle optimizer (CO), where the proposed ESMOA provides the best performance. Furthermore, the findings of the proposed cascaded PD-PI controller based on the ESMOA outperform previous published PID and PI controllers adjusted using numerous contemporary techniques. Full article

This paper proposes a new cascaded fractional-order controller (CC-FOC) to solve the load frequency control (LFC) problem of an interconnected power system. The CC-FOC consists of a three-degree-of-freedom fractional-order proportional-integral-differential (3DOF-FOPID) controller and a fractional-order proportional-integral (FOPI) controller. Each area of the two-area interconnected power system in this study consists of a thermal unit, a hydro unit, a diesel unit, and a doubly-fed induction generator (DFIG). The enhanced particle swarm optimization (PSO) and gravitational search algorithm (GSA) under the chaotic map optimization (CPSOGSA) technique are used to optimize the controller gains and parameters to enhance the load frequency control performance of the cascade controller. Moreover, simulation experiments are conducted for the interconnected power system under load perturbation and random wind speed fluctuations. The simulation results demonstrate that the proposed cascaded fractional-order controller outperforms the traditional proportional-integral-differential (PID) controller and three other fractional-order controllers in terms of LFC performance. The suggested cascade controller displays strong dynamic control performance and the resilience of the cascade fractional-order controller by adjusting the load disturbance and analyzing the system characteristics. Full article

This paper proposed an image algorithm based on a cascaded chaotic system to improve the performance of the encryption algorithm. Firstly, this paper proposed an improved cascaded two-dimensional map 2D-Cosine-Logistic-Sine map (2D-CLSM). Cascade chaotic system offers good advantages in terms of key space, complexity and sensitivity to initial conditions. By using the control parameters and initial values associated with the plaintext, the system generates two chaotic sequences associated with the plaintext image. Then, an S-box construction method is proposed, and an encryption method is designed based on the S-box. Encryption is divided into bit-level encryption and pixel-level encryption, and a diffusion method was devised to improve security and efficiency in bit-level encryption. Performance analysis shows that the encryption algorithm has good security and is easily resistant to various attacks. Full article

Dual-stage cascaded dc systems are some of the most widely applied power interfaces in dc distributed power systems. However, in some practical situations, these systems might be unstable, especially if they incorporate tightly regulated load converters that operate as constant power loads (CPLs), whose power fluctuations could exert a cascading impact on the operation of the systems. Existing studies tend to describe the instability phenomena using bifurcation diagram analysis and the loci of eigenvalue analysis. However, it is usually difficult to derive the explicit expressions of the stability criterion. This paper addresses the large-signal stability issue of the dual-stage cascaded dc systems from a standpoint of load power and obtains the explicit form large-signal stability boundary in terms of load power by using Lyapunov-type mixed potential theory. Moreover, the prototype dual-stage cascaded dc system, in which the control strategies for the feeder converter and the load converter are different, is used as an example in this study. According to the results, the system remains stable when the load power is in [5.8, 23.2] W. When load power is less than 5.8 W or increased to [23.2, 32.8] W, the system is in a period-2 subharmonic oscillation state. Moreover, when the load power exceeds 32.8 W, the system falls into a chaotic state. The deduced boundary is highly consistent with the analysis results of both a bifurcation diagram and Jacobian matrix based analysis. Finally, both circuit-level simulation and experimental results validate the effectiveness of the load power stability boundary. Full article