Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System by Nadjette Debbouche, Adel Ouannas, Iqbal M. Batiha, Giuseppe Grassi, Mohammed K. A. Kaabar, Hadi Jahanshahi, Ayman A. Aly, Awad M. Aljuaid

“…Several numerical simulations are implemented, and the obtained findings are illustrated through constructing bifurcation diagrams, computing Lyapunov exponents, calculating Lyapunov dimensions, and sketching the phase portraits in 2D and 3D projections.…”
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Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios by A. A. Elsadany, A. M. Yousef, S. A. Ghazwani, A. S. Zaki

“…Finally, through bifurcation diagrams, maximal Lyapunov exponents, and phase portraits, we uncover a diversity of dynamical characteristics, including limit cycles, periodic solutions, and chaotic attractors.…”
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Entre campagne publicitaire et films d’auteur : douze paysages urbains italiens au cinéma by Olivier Gaudin

“…12 Registi per 12 città (1989) is a commissioned promotional film comprising twelve portraits of cities, produced by twelve famous Italian filmmakers before the 14th World Cup (Italia’90). …”
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Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback by Shao-Fang Wen, Ju-Feng Chen, Shu-Qi Guo

“…The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. …”
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Qualitative Analysis of Class of Fractional-Order Chaotic System via Bifurcation and Lyapunov Exponents Notions by Ndolane Sene

“…In a fractional context, the phase portraits will be obtained with a predictor-corrector numerical scheme method. …”
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At the dawn of the White Movement (about A. S. Puchenkov’s monograph «The first year of the Volunteer Army: from the emergence of the “Alekseevskaya Organization” to the formation... by D. A. Bazhanov

“…Puchenkov allows to get a comprehensive picture of the military and political formation of the White Movement in the South of Russia, highlights the main factors for the success of the counter-revolution in 1918, presents vivid portraits of its leaders, revealing their difficult relationships. …”
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THE PHENOMENON OF LANGUAGE GAMES AS COLLEGE STUDENTS RESPONSES TO THE REVISED CRIMINAL CODE DRAFT 2019: A SOCIOLINGUISTICS STUDY by Nurul Nisfu Syahriy, Ridwan Hanafiah, Rudy Sofyan

“…For this reason, the data used are portraits of posters and banners sourced from various cities in Indonesia with various forms of utterance. …”
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Reading the Background: The Textual and the Visual in Steve Tomasula’s The Book of Portraiture by Pawel Frelik

“…Its central preoccupation with titular portraits, or images of humanity in general, and the universal impulse to picture ourselves in paint, dreams, photography, electronic data and genetic code is first and foremost deployed in a series of interlocked and highly complex narrative chapters. …”
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Modeling and Dynamical Analysis of the Water Resources Supply-Demand System: A Case Study in Haihe River Basin by Chongli Di, Xiaohua Yang

“…Finally, the dynamical analysis of the system is further studied by Lyapunov-exponent, phase portraits, and Lyapunov exponent theory. Numerical simulation results demonstrate that the proposed water resources supply-demand system is in a steady state and is suitable for simulating the dynamical characteristics of a complex water supply and demand system. …”
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Bifurcation Study of Thin Plate with an All-Over Breathing Crack by Lihua Chen, Jian Xue, Zhijie Zhang, Wei Zhang

“…Lastly, the waveforms, bifurcation diagrams, and phase portraits of the model are gained by the Runge-Kutta method. …”
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On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator by Shahram Rezapour, Chernet Tuge Deressa, Sina Etemad

“…It is shown using phase-space portraits and time-series orbit figures that the system is sensitive to derivative order change, parameter change, and small initial condition change. …”
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Threshold for Chaos of a Duffing Oscillator with Fractional-Order Derivative by Wuce Xing, Enli Chen, Yujian Chang, Meiqi Wang

“…The largest Lyapunov exponents are provided, and some other typical numerical simulation results, including the time histories, frequency spectrograms, phase portraits, and Poincare maps, are presented and compared. …”
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Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs by Fei Yu, Zinan Zhang, Li Liu, Hui Shen, Yuanyuan Huang, Changqiong Shi, Shuo Cai, Yun Song, Sichun Du, Quan Xu

“…The dynamic characteristics of the system are studied in terms of equilibrium point, perpetual point, bifurcation diagram, Lyapunov exponential spectrum, phase portraits, and spectral entropy. This system is of the group of systems that have coexisting attractors. …”
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Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes by Matteo Strozzi, Francesco Pellicano

“…The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs are investigated. …”
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An Improved Particle Swarm Optimization-Powered Adaptive Classification and Migration Visualization for Music Style by Xiahan Liu

“…This visual effect can help users generate unique and personalized portraits with music; it can also be widely used by artists to express the relationship between music and vision. …”
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A Four-Zone Model and Nonlinear Dynamic Analysis of Solution Multiplicity of Buoyancy Ventilation in Underground Building by Yuxing Wang, Chunyu Wei

“…We find that the unstable equilibrium point interval is divided into two different subintervals corresponding to the saddle point of index 2 and the saddle focal equilibrium point of index 2, respectively. Finally, the phase portraits and vector field diagrams for the two scenarios are given.…”
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EVOLUTION OF THE ROTATIONAL MOTION OF A SATELLITE WITH FLEXIBLE VISCOELASTIC RODS ON THE ELLIPTIC ORBIT by E. V. Sadovnikova, A. V. Shatina

“…For each such class of solutions phase portraits are built. It is shown that in the process of dissipative evolution caused by energy dissipation in rods, the angle between the vector of the angular momentum of the satellite's rotational motion and the normal to the orbital plane decreases to zero. …”
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A Novel Procedure in Scrutinizing a Cantilever Beam with Tip Mass: Analytic and Bifurcation by Asma Alanazy, Galal M. Moatimid, T. S. Amer, Mona A. A. Mohamed, M. K. Abohamer

“…Bifurcation diagrams, phase portraits, and Poincaré maps are used to study the chaotic behavior of the model, revealing various types of motion, including periodic and chaotic behavior.…”
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Nonlinear Dynamics of the High-Speed Rotating Plate by Minghui Yao, Li Ma, Wei Zhang

“…Bifurcation diagram, phase portraits, waveforms and power spectrum prove that periodic motion and chaotic motion exist in nonlinear vibration of the rotating cantilever composite plate.…”
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Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors by Fei Yu, Li Liu, Hui Shen, Zinan Zhang, Yuanyuan Huang, Changqiong Shi, Shuo Cai, Xianming Wu, Sichun Du, Qiuzhen Wan

“…Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. …”
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