Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation by Musheer Ahmad, Eesa Al-Solami

“…Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration of substitution-box matrix over the enormously large problem space of 256!. …”
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Dynamics and Complexity Analysis of Fractional-Order Chaotic Systems with Line Equilibrium Based on Adomian Decomposition by Heng Chen, Tengfei Lei, Su Lu, WenPeng Dai, Lijun Qiu, Lin Zhong

“…That is, integer-order systems do not have the phenomenon of attractors coexistence, while fractional-order systems have it.…”
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Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series by Liu Hai, Song Yong, Du Qingfu

“…Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. …”
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Research on Supply Chain Stability Driven by Consumer’s Channel Preference Based on Complexity Theory by Yi Tian, Junhai Ma, Wandong Lou

“…In addition, the dynamic features of the system are simulated by 2D bifurcation diagram, the largest Lyapunov exponent, attractor variation, and time series. The simulation results suggest that if the adjustment speeds of the wholesale prices and sales commissions change drastically, the system would fall into a chaotic state. …”
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Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service by Junhai Ma, Weiya Di, Hao Ren

“…The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. …”
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A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing by Arthanari Ramesh, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain

“…As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. …”
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Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect by Na Min, Hongyang Zhang, Xiaobin Gao, Pengyu Zeng

“…Using topological equivalent and the blow-up method, we proved that the origin was the attractor, and a defined basin of attraction was given. …”
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A New Simple Chaotic Lorenz-Type System and Its Digital Realization Using a TFT Touch-Screen Display Embedded System by Rodrigo Méndez-Ramírez, Adrian Arellano-Delgado, César Cruz-Hernández, Rigoberto Martínez-Clark

“…The proposed system generates a chaotic attractor with the variation of two parameters. Analytical and numerical studies of the dynamic properties to generate chaos, for continuous version (CV) and discretized version (DV), for the new chaotic system (NCS) were conducted. …”
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Sequence of Routes to Chaos in a Lorenz-Type System by Fangyan Yang, Yongming Cao, Lijuan Chen, Qingdu Li

“…When n is odd, the n isolated sub-branches are from a period-n limit cycle, followed by twin period-n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. …”
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The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern by Huang Yi-min, Li Qiu-xiang, Zhang Yu-hao

“…The stability of the system and the influences of different parameter values on utilities are analyzed emphatically using game theory and nonlinear dynamic theory, such as 2D and 3D bifurcation diagram, parameter plot basin, chaos attractor, and sensitivity to initial value. The results find that the system is more likely to lose stability and fall into chaos with the customer demand fluctuating greatly. …”
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Robustness of Supercavitating Vehicles Based on Multistability Analysis by Yipin Lv, Tianhong Xiong, Wenjun Yi, Jun Guan

“…Results of the research disclose that the supercavitating system has three stable states in some regions of parameters space, namely, stable, periodic, and chaotic states, while in other regions it has various multistability, such as coexistence of two types of stable equilibrium points, coexistence of a limit cycle with a chaotic attractor, and coexistence of 1-periodic cycle with 2-periodic cycle. …”
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On the Price Dynamics of a Two-Dimensional Financial Market Model with Entry Levels by En-Guo Gu

“…The existence and stability conditions of periodic attractors and other bounded attractors are derived by using qualitative and quantitative methods, theoretical analysis, and numerical simulation. …”
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Segmentation of Myocardial Boundaries in Tagged Cardiac MRI Using Active Contours: A Gradient-Based Approach Integrating Texture Analysis by Aymeric Histace, Bogdan Matuszewski, Yan Zhang

“…Texture analysis allows us to define energy maps more efficient than those usually used in active contours methods where attractor is often based on gradient and which were useless in our case of study, for quality of tagged cardiac MRI is very poor.…”
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Experimental evaluation of DC-DC buck converter based on adaptive fuzzy fast terminal synergetic controller by Zahira Anane, Badreddine Babes, Noureddine Hamouda, Omar Fethi Benaouda, Saud Alotaibi, Thabet Alzahrani, Dessalegn Bitew Aeggegn, Sherif S. M. Ghoneim

“…Abstract This study suggests an enhanced version of the adaptive fuzzy fast terminal synergetic controller (AF-FTSC) for controlling the uncertain DC/DC buck converter based on the synergetic theory of control (STC) and newly developed terminal attractor technique (TAT). The benefits of the proposed SC algorithm involve the features of finite-time convergence, unaffected by parameter variations, and chattering-free phenomenon. …”
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Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control by S. S. Askar, A. Al-khedhairi

“…This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.…”
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Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition by Jianli Xiao, Hanli Xiao, Xinchang Zhang, Xiang You

“…With the help of bifurcation diagram, Lyapunov exponent, and strange attractor, the stability of the two-sided market competition model is simulated. …”
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Research on Grid Scroll Chaotic Extended Sequence Algorithm and Its Circuit Implementation for F-OFDM System by Yingjie Ma, Ya Li, Geng Zhao, Ping Zeng, Yatao Yang

“…Moreover, the hardware experimental results produce at 2 × 2 × 2-grid multiscroll chaotic attractor, which further proves the physical realization of the proposed system. …”
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Sustainable Development and World Politics by A. Ursul, D. Kalyuzhnaya

“…The real global integrity of the world political system serves as a global attractor of this evolutionary transformation, and this aspect represents the specific pattern of all global processes. …”
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Predictive Analysis of Economic Chaotic Time Series Based on Chaotic Genetics Combined with Fuzzy Decision Algorithm by Xiuge Tan

“…The phase space of its reconstructed chaotic attractor has high-precision predictability and can find orderly processes from changeable economic results, which in turn can be used to analyze and predict the complex economic chaotic time series. …”
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A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisis by Jorge Duarte, Cristina Januário, Nuno Martins

“…A particular type of these transitions occurs when the size of a chaotic attractor suddenly changes. In this article, we present such a transition through the observation of a chaotic interior crisis in the Deng bursting-spiking model for the glucose-induced electrical activity of pancreatic $β $-cells. …”
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