A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos by Chunmei Wang, Chunhua Hu, Jingwei Han, Shijian Cang

“…Numerical simulation techniques, including phase portraits and Lyapunov exponents, are used to investigate its basic dynamical behavior. …”
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Abundant Bounded and Unbounded Solitary, Periodic, Rogue-Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model by Mohammad Mobarak Hossain, Alrazi Abdeljabbar, Harun-Or Roshid, Md. Mamunur Roshid, Abu Naim Sheikh

“…We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of all phase portraits, we originate bounded and unbounded solitary, periodic, and periodic rogue-type wave solutions of the KG model. …”
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Bifurcation of Travelling Wave Solutions of the Generalized Zakharov Equation by Masoud Mosaddeghi

“…In each of these parametric regions the exact explicit parametric representation of all solitary, kink (antikink), and periodic wave solutions as well as their numerical simulation and their corresponding phase portraits are obtained.…”
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Explicit Wave Solutions and Qualitative Analysis of the (1 + 2)-Dimensional Nonlinear Schrödinger Equation with Dual-Power Law Nonlinearity by Qing Meng, Bin He, Zhenyang Li

“…The (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented.…”
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Peakon, Solitary and Smooth Periodic Wave Solutions for a Modification of the K(2,2) Equation by Qing Meng, Bin He

“…We consider a modification of the K(2,2) equation ut=2uuxxx+2kuxuxx+2uux using the bifurcation method of dynamical systems and the method of phase portraits analysis. From dynamic point of view, some peakons, solitary, and smooth periodic waves are found and their exact parametric representations are presented. …”
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Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay by Xia Huang, Zhen Wang, Yuxia Li

“…The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.…”
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Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System by Yanqin Xiong, Maoan Han

“…We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. …”
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Bifurcation and Chaos Prediction in Nonlinear Gear Systems by Anooshirvan Farshidianfar, Amin Saghafi

“…The numerical simulation of the system including bifurcation diagram, phase plane portraits, Fourier spectra, and time histories is considered to confirm the analytical predictions for the occurrence of homoclinic bifurcation and chaos in nonlinear gear systems.…”
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On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields by Michail P. Markakis, Panagiotis S. Douris

“…Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.…”
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Universality of oscillation theory laws. types and role of mathematical models by Polina S. Landa

“…It is suggested that all models of concrete systems be separated into four categories: models – “portraits” of investigated systems, models of the type of “black box”, aggregating models, and models of certain phenomena which can occur in real systems. …”
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Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation by F. Waffo Tchuimmo, J. B. Gonpe Tafo, A. Chamgoue, N. C. Tsague Mezamo, F. Kenmogne, L. Nana

“…Under some constraints of parameters, equilibrium points are obtained and phase portraits have been plotted. The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. …”
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Exact Traveling Wave Solutions and Bifurcation of a Generalized (3+1)-Dimensional Time-Fractional Camassa-Holm-Kadomtsev-Petviashvili Equation by Zhigang Liu, Kelei Zhang, Mengyuan Li

“…Furthermore, the phase portraits of the dynamical system and the remarkable features of the solutions are demonstrated via interesting figures.…”
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The execution of wax-resin linings by Johannes Albertus Hesterman (1848-1916) and sons by Saskia van Oudheusden

“…Five seventeenth-century portraits from the collection in the Amsterdam Museum, which were lined by the Hestermans in the years 1907-8, were investigated. …”
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Dynamics Analysis and Control of a Five-Term Fractional-Order System by Li-xin Yang, Xiao-jun Liu

“…Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. …”
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Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach by Jie Song, Feng Li, Mingji Zhang

“…By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. …”
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Stability, Bifurcation, and Quenching Chaos of a Vehicle Suspension System by Chun-Cheng Chen, Shun-Chang Chang

“…The nonlinear dynamics were determined using bifurcation diagrams, phase portraits, Poincaré maps, frequency spectra, and Lyapunov exponents. …”
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Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives by Shalu Saini, Rajeev Kumar, null Deeksha, Rishu Arora, Kamal Kumar

“…The theory of bifurcation has been utilized in the reduced form to check the stability and nature of critical points by transforming the equations into an autonomous system. Some phase portraits have been drawn at different critical points by the use of maple.…”
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Complex Dynamics of an Adnascent-Type Game Model by Baogui Xin, Junhai Ma, Qin Gao

“…Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.…”
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