Nikolai A. Magnitskii^*

FDMP-Fluid Dynamics & Materials Processing, Vol.21, No.7, pp. 1529-1544, 2025, DOI:10.32604/fdmp.2025.067021 - 31 July 2025

Abstract This paper presents both analytical and numerical studies of the conservative Sawada–Kotera equation and its dissipative generalization, equations known for their soliton solutions and rich chaotic dynamics. These models offer valuable insights into nonlinear wave propagation, with applications in fluid dynamics and materials science, including systems such as liquid crystals and ferrofluids. It is shown that the conservative Sawada–Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles, as well as two- and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation (ODE) system. For the dissipative generalized Sawada–Kotera equation, chaotic More >

Ashish Rayal¹, Priya Dogra¹, Sabri T. M. Thabet^2,3,4,*, Imed Kedim⁵, Miguel Vivas-Cortez^6,*

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 1895-1925, 2025, DOI:10.32604/cmes.2025.060989 - 30 May 2025

Abstract The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns, biological systems, and secure communications. So, this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets. The Caputo fractional Rössler attractor model is simulated into two categories, (i) Asymmetric and (ii) Symmetric. The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of More >

Mariya Shiryaeva¹, Mariya Subbotina², Stanislav Subbotin^1,*

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.4, pp. 787-802, 2024, DOI:10.32604/fdmp.2024.048165 - 28 March 2024

Abstract This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends. In this setting, the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius. Three different regimes are found: inertial wave attractor, global oscillations (the cavity’s resonant modes) and regime of symmetric reflection of wave beams. In linear wave regimes, a steady single vortex elongated along the rotation axis is generated. The location of the wave’s interaction with the sloping ends determines the vortex position and More >

Mohamad Afendee Mohamed¹, Talal Bonny², Aceng Sambas³, Sundarapandian Vaidyanathan⁴, Wafaa Al Nassan², Sen Zhang⁵, Khaled Obaideen², Mustafa Mamat¹, Mohd Kamal Mohd Nawawi^6,*

CMC-Computers, Materials & Continua, Vol.75, No.3, pp. 5987-6006, 2023, DOI:10.32604/cmc.2023.035668 - 29 April 2023

Abstract In recent years, there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle, butterfly, heart and apple. This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve. The proposed chaotic system has two quadratic, two cubic and two quartic nonlinear terms. It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points. It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but… More >

Xiang Yu¹, Chonghua Wang², Xiaojing Zheng^3,*, Chaoyu Zeng⁴, Brij B. Gupta^5,6,7

CMC-Computers, Materials & Continua, Vol.75, No.1, pp. 2079-2099, 2023, DOI:10.32604/cmc.2023.034118 - 06 February 2023

Abstract This paper constructs a non-cooperative/cooperative stochastic differential game model to prove that the optimal strategies trajectory of agents in a system with a topological configuration of a Multi-Local-World graph would converge into a certain attractor if the system’s configuration is fixed. Due to the economics and management property, almost all systems are divided into several independent Local-Worlds, and the interaction between agents in the system is more complex. The interaction between agents in the same Local-World is defined as a stochastic differential cooperative game; conversely, the interaction between agents in different Local-Worlds is defined as… More >

Shui-Hua Wang¹, Muhammad Attique Khan², Ziquan Zhu¹, Yu-Dong Zhang^1,*

Computer Systems Science and Engineering, Vol.45, No.1, pp. 21-34, 2023, DOI:10.32604/csse.2023.031330 - 16 August 2022

Abstract Community-acquired pneumonia (CAP) is considered a sort of pneumonia developed outside hospitals and clinics. To diagnose community-acquired pneumonia (CAP) more efficiently, we proposed a novel neural network model. We introduce the 2-dimensional wavelet entropy (2d-WE) layer and an adaptive chaotic particle swarm optimization (ACP) algorithm to train the feed-forward neural network. The ACP uses adaptive inertia weight factor (AIWF) and Rossler attractor (RA) to improve the performance of standard particle swarm optimization. The final combined model is named WE-layer ACP-based network (WACPN), which attains a sensitivity of 91.87 ± 1.37%, a specificity of 90.70 ± 1.19%, a precision of More >

Saad Adjal^1,*, Sabiha Aklouche-Benouaguef¹, Belkacem Zeghmati²

FDMP-Fluid Dynamics & Materials Processing, Vol.18, No.5, pp. 1389-1397, 2022, DOI:10.32604/fdmp.2022.021619 - 27 May 2022

Abstract Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30∘ is investigated numerically. The vertical walls are differentially heated, and the horizontal walls are adiabatic. The effect of Rayleigh number on heat transfer and on the road to chaos is analyzed. The natural heat transfer and the Darcy Brinkman equations are solved by using a finite volume method and a Tri Diagonal Matrix Algorithm (TDMA). The results are obtained for a porosity equal to 0.45, a Darcy number and a Prandtl respectively equal to 10⁻³ and More >

R. Anitha^*, B. Vijayalakshmi

CMC-Computers, Materials & Continua, Vol.72, No.2, pp. 3447-3463, 2022, DOI:10.32604/cmc.2022.021519 - 29 March 2022

Abstract In the current scenario, data transmission over the network is a challenging task as there is a need for protecting sensitive data. Traditional encryption schemes are less sensitive and less complex thus prone to attacks during transmission. It has been observed that an encryption scheme using chaotic theory is more promising due to its non-linear and unpredictable behavior. Hence, proposed a novel hybrid image encryption scheme with multi-scroll attractors and quantum chaos logistic maps (MSA-QCLM). The image data is classified as inter-bits and intra-bits which are permutated separately using multi scroll attractor & quantum logistic… More >

Yong Xiao¹, Xin Jin¹, Jingfeng Yang², Yanhua Shen^3,*, Quansheng Guan⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 1293-1313, 2021, DOI:10.32604/cmes.2021.012562 - 19 February 2021

Abstract User-transformer relations are significant to electric power marketing, power supply safety, and line loss calculations. To get accurate user-transformer relations, this paper proposes an identification method for user-transformer relations based on improved quantum particle swarm optimization (QPSO) and Fuzzy C-Means Clustering. The main idea is: as energy meters at different transformer areas exhibit different zero-crossing shift features, we classify the zero-crossing shift data from energy meters through Fuzzy C-Means Clustering and compare it with that at the transformer end to identify user-transformer relations. The proposed method contributes in three main ways. First, based on the… More >

Hong Qian^∗, Hao Ge^†

Molecular & Cellular Biomechanics, Vol.9, No.1, pp. 1-30, 2012, DOI:10.3970/mcb.2012.009.001

Abstract Biochemical reaction systems in mesoscopic volume, under sustained environmental chemical gradient(s), can have multiple stochastic attractors. Two distinct mechanisms are known for their origins: (a) Stochastic single-molecule events, such as gene expression, with slow gene on-off dynamics; and (b) nonlinear networks with feedbacks. These two mechanisms yield different volume dependence for the sojourn time of an attractor. As in the classic Arrhenius theory for temperature dependent transition rates, a landscape perspective provides a natural framework for the system's behavior. However, due to the nonequilibrium nature of the open chemical systems, the landscape, and the attractors More >