On the Investigation of State Space Reconstruction of Nonlinear Aeroelastic Response Time Series by Flávio D. Marques, Eduardo M. Belo, Vilma A. Oliveira, José R. Rosolen, Andréia R. Simoni

“…The method of delays is used to identify an embedded attractor in the state space from experimentally acquired aeroelastic response time series. …”
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Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control by J. Humberto Pérez-Cruz, Pedro A. Tamayo-Meza, Maricela Figueroa, Ramón Silva-Ortigoza, Mario Ponce-Silva, R. Rivera-Blas, Mario Aldape-Pérez

“…This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. …”
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BEAUTY IN MATHEMATICAL EDUCATION: SYNERGETIC WORLDVIEW by V. A. Testov

“…The synergetrics as a general scientific theory about self-organisation of complex systems allows us to give another interpretation of beauty – as a kind of attractor, the result of self-organisation of nature or theflight of human thought. …”
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Principal component analysis and its generalizations for any type of sequence (PCA-Seq) by V. M. Efimov, K. V. Efimov, V. Y. Kovaleva

“…By the beginning of the 1980s, Takens had shown that for a dynamical system such a method makes it possible to obtain an attractor from observing only one of these variables, thereby bringing the method to a powerful theoretical basis. …”
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A physically-based formulation for texture evolution during dynamic recrystallization. A case study of ice by Chauve, Thomas, Montagnat, Maurine, Dansereau, Véronique, Saramito, Pierre, Fourteau, Kévin, Tommasi, Andréa

“…This formulation relies on an orientation attractor that maximizes the resolved shear stress on the easiest slip system in the crystal. …”
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Beyond Chaos in Fractional-Order Systems: Keen Insight in the Dynamic Effects by José Luis Echenausía-Monroy, Luis Alberto Quezada-Tellez, Hector Eduardo Gilardi-Velázquez, Omar Fernando Ruíz-Martínez, María del Carmen Heras-Sánchez, Jose E. Lozano-Rizk, José Ricardo Cuesta-García, Luis Alejandro Márquez-Martínez, Raúl Rivera-Rodríguez, Jonatan Pena Ramirez, Joaquín Álvarez

“…By quantifying the convex envelope generated by the 2D projection of the system into all its phase portraits, the changes in the area of the system, as well as the volume of the attractor, are characterized. The results are compared with standard metrics for the study of chaotic systems, such as the Kaplan–Yorke dimension and the fractal dimension, and we also evaluate the frequency fluctuations in the dynamical response. …”
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Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand by S. S. Askar, A. Ibrahim, A. A. Elsadany

“…Four forms of coexistence of attractors are demonstrated by the basin of attraction, which is the coexistence of periodic attractors and chaotic attractors, the coexistence of periodic attractors and quasiperiodic attractors, and the coexistence of several chaotic attractors. …”
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Dynamics of Generalized Tachyon Field in Teleparallel Gravity by Behnaz Fazlpour, Ali Banijamali

“…In contrast with tachyonic teleparallel dark energy model that has no scaling attractors, here we find some scaling attractors which means that the cosmological coincidence problem can be alleviated. …”
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Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps by ZaiTang Huang, ChunTao Chen

“…We study the stability, attractors, and bifurcation of stochastic Rayleigh-van der Pol equations with jumps. …”
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Synthesizing fractal images by means of shift dynamical systems by Jonas Valantinas, Rokas Valantinas, Tomas Žumbakis

“… In this paper, the adaptation problem of the time escape algorithm to the special class of fractal images (attractors of iterated function systems) and the necessary mathematical context are ana­lysed. …”
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Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams by Lilian Huang, Wenju Yao, Jianhong Xiang, Zefeng Zhang

“…Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.…”
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Qualitative Study of a 4D Chaos Financial System by Fuchen Zhang, Gaoxiang Yang, Yong Zhang, Xiaofeng Liao, Guangyun Zhang

“…These results are useful in estimating the Lyapunov dimension of attractors, Hausdorff dimension of attractors, chaos control, and chaos synchronization. …”
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Mathematical analysis of a HIV model with frequency dependence and viral diversity by Shingo Iwami, Shinji Nakaoka, Yasuhiro Takeuchi

“…The model has very complex mathematicalstructures such as limit cycle, quasi-periodic attractors, chaotic attractors, andso on. To understand the complexity we investigate the global behavior of themodel and demonstrate the existence and stability conditions of the equilibria.Further we give some theoretical considerations obtained by our mathematicalmodel to HIV infection.…”
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Discrete dynamics in transitional economies by J. Barkley Rosser, Jr., Marina Vcherashnaya Rosser

“…During recovery, transitional cobweb labor market dynamics exhibit chaos, fractal basin boundaries between coexisting non-chaotic attractors, discontinuous phase transitions, strange attractors, and cascades of infinitely many period-doubling bifurcations.…”
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Complex Dynamics in Generalized Hénon Map by Meixiang Cai

“…The numerical simulations show the consistence with the theoretical analysis and reveal some new complex phenomena which can not be given by theoretical analysis, such as the invariant cycles which are irregular closed graphics, the six and forty-one coexisting invariant cycles, and the two, six, seven, nine, ten, and thirteen coexisting chaotic attractors, and some kinds of strange chaotic attractors.…”
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Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators by Ahmad Taher Azar, Ngo Mouelas Adele, Kammogne Soup Tewa Alain, Romanic Kengne, Fotsin Hilaire Bertrand

“…The parameters window in which the jerk system exhibits the unusual and striking feature of multiple attractors (e.g., coexistence of six disconnected periodic chaotic attractors and three-point attraction) is investigated. …”
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Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems by Enzeng Dong, Guanghan Liu, Zenghui Wang, Zengqiang Chen

“…Since the conservative chaotic system (CCS) has no general attractors, conservative chaotic flows are more suitable for the chaos-based secure communication than the chaotic attractors. …”
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Analysis of Chaotic Features in Dry Gas Seal Friction State Using Acoustic Emission by Shuai Zhang, Xuexing Ding, Jinlin Chen, Shipeng Wang, Lanxia Zhang

“…The maximum Lyapunov exponent, correlation dimension, K-entropy, and attractors of the AE signals throughout the operation of the dry gas seal are calculated and analyzed. …”
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No Chattering and Adaptive Sliding Mode Control of a Fractional-Order Phase Converter with Disturbances and Parameter Uncertainties by Karthikeyan Rajagopal, Riessom Weldegiorgis, Anitha Karthikeyan, Prakash Duraisamy, Goitom Tadesse

“…Using forward and backward continuation, various coexisting attractors and the property of multistability are discussed. …”
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