Market Share Delegation in a Bertrand Duopoly: Synchronisation and Multistability by Luciano Fanti, Luca Gori, Cristiana Mammana, Elisabetta Michetti

“…In addition, there exist multiple attractors so that even starting with similar conditions may end up generating very different dynamic patterns.…”
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Chaos in a Predator-Prey System with Impulsive Perturbations and Stage Structure for the Predator by Bin Zhang, Shuai Shi, Woye Liu

“…Furthermore, by using the method of numerical simulation, the influence of the impulsive control strategy on the inherent oscillation is investigated, which shows rich complex dynamic (such as periodic doubling bifurcation, periodic halving bifurcation, nonunique attractors, chaos, and periodic windows).…”
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Coexistence of the Bandcount-Adding and Bandcount-Increment Scenarios by Viktor Avrutin, Michael Schanz, Björn Schenke

“…One of them is organized by the period-adding scenario whereas the other one by the period-increment scenario with coexisting attractors. In the chaotic domain, the influence of both adjacent periodic domains leads to the coexistence of the recently discovered bandcount adding and bandcount-increment scenarios. …”
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A New Fractional-Order Chaotic Complex System and Its Antisynchronization by Cuimei Jiang, Shutang Liu, Chao Luo

“…We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. …”
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The Characteristic Relation in Two-Dimensional Type I Intermittency by Juan Colman, Sergio Elaskar

“…This investigation is carried out numerically, concentrating on the system’s attractors, bifurcation diagrams, and the characteristic relation associated with type I intermittency. …”
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Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control by Bo Yan, Shaobo He, Shaojie Wang

“…It shows that the minimum order for chaos of the fractional-order centrifugal flywheel governor system is q = 0.97, and the system has rich dynamics and produces multiple coexisting attractors. Moreover, the system is controlled by introducing the adaptive controller which is proved by the Lyapunov stability theory. …”
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Chaos and Dynamics Induced by the Amplitude of Load Torque: Analysis and Control by Arnaud Ngonting Topy, Justin Roger Mboupda Pone, Alex Stephane Kemnang Tsafack, Romanic Kengne

“…The analysis shows that under some conditions, varying amplitude of the load torque, PMSM presents period doubling route to chaos with one and double-scroll attractors and bursting oscillations. We use the self-feedback delay controller to stabilize the output trajectory by forcing to the periodic solution. …”
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Periodic Motion and Transition of a Vibro‐Impact System with Multilevel Elastic Constraints by Jie Ding, Chao Wang, Wangcai Ding

“…At the same time, combined with the cell mapping method, the coexistence of attractors induced due to grazing bifurcation, saddle-node bifurcation, and boundary crisis is studied. …”
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Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality by Junhai Ma, Hongwu Wang

“…Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. …”
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Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators by Gerold Baier, Sven Sahle

“…We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. …”
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Nonlinear Dynamical Analysis of Hydraulic Turbine Governing Systems with Nonelastic Water Hammer Effect by Junyi Li, Qijuan Chen

“…In addition, chaotic characteristics of the system with different system parameters are studied extensively and presented in the form of bifurcation diagrams, time waveforms, phase space trajectories, Lyapunov exponent, chaotic attractors, and Poincare maps. Good correlation can be found between the model predictions and theoretical analysis. …”
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Medium Affect Desire: Hybridising Real Virtual and the Actualised through Affective Medium Ecology by Marc Boumeester

“…This new materialistic, non-anthropocentric liberty of affect is creating an arena of strange attractors and other topological vector fields in which our own unconscious drive is as effective as that of the steel ball in a pinball machine. …”
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Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges by Wei Li, Chunrui Zhang, Mi Wang

“…Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.…”
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Computation of the topological entropy in chaotic biophysical bursting models for excitable cells by Jorge Duarte, Luís Silva, J. Sousa Ramos

“…With results from symbolic dynamics, we characterize the topological entropy of one-dimensional maps that describe the salient dynamics on the attractors. The analysis of the variation of this important numerical invariant with the parameters of the systems allows us to quantify the complexity of the phenomenon and to distinguish different chaotic scenarios. …”
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Chaotic motion of particles in the spacetime of a Kerr black hole immersed in swirling universes by Deshui Cao, Lina Zhang, Songbai Chen, Qiyuan Pan, Jiliang Jing

“…Moreover, we observe clearly that, regardless of the spin parameter, there exist some self-similar fractal fine structures in the basins boundaries of attractors for the spacetime of a black hole immersed in swirling universes. …”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model by Xueli Chen, Lishun Ren

“…More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. …”
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Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function by Hui Li, Wei Zhou, Tong Chu

“…With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures (also called Isoperiodic Stable Structures) and different shape basins of attraction of coexisting attractors. The eye-shaped structures appear where the period-doubling and period-halving bifurcations occur. …”
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Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium by Xiong Wang, Viet-Thanh Pham, Christos Volos

“…It is worth noting that the new system generates chaotic behavior as well as hidden attractors. Dynamics of the system with closed curve equilibrium have been investigated by using phase portraits, bifurcation diagram, maximal Lyapunov exponents, and Kaplan–York dimension. …”
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Numerical Analysis of Discrete Switching Prey-Predator Model for Integrated Pest Management by Changcheng Xiang, Yi Yang, Zhongyi Xiang, Wenjie Qin

“…Besides, numerical bifurcation analyses show that the switching discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, the effects of key parameters on the switching frequencies and switching times are discussed and the sensitivity analysis of varying parameter values for mean switching times has also been given. …”
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Analysis of Rattleback Chaotic Oscillations by Michael Hanias, Stavros G. Stavrinides, Santo Banerjee

“…The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors’ invariant parameters.…”
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