Stable-to-unstable transition in quantum friction by Daigo Oue, J. B. Pendry, Mário G. Silveirinha

“…Here, we develop a fully quantum-mechanical theory without perturbative approximations, and we unveil the transition from stable to unstable regimes of the quantum friction setup. …”
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A Dynamic Landslide Warning Model Based on Grey System Theory by Ke Ma, He Weng, Yumin Chen, Saeed Sarajpoor, Yang Shen

“…This paper proposes a dynamic landslide warning model that integrates the concept of risk with grey system theory, using a small amount of real-time monitoring data. …”
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Study on Catastrophe Instability of Support System in Gypsum Goaf Based on Energy Dissipation Theory by Yuejin Zhou, Xiaoding Xu, Xiaotong Li, Meng Li, Yugui Yang

“…Through establishing a cusp catastrophe model based on energy theory, the new criterion for instability was obtained which is related with geometric stiffness and system energy dissipation. …”
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Development and evaluation of the organization`s logistics strategy based on the application of bifurcation theory by M. Yu. Uchirova, L. A. Ilin, S. V. Khudyakov

“…The authors reveal that the bifurcation theory allows you to determine the conditionality of a qualitative dynamic change in the behavior of a logistics system by an infinitesimal change in certain parameters of the system. …”
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Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics by Till D. Frank

“…At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. …”
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From Behaviorism to Neoconstructivism: A Review of Educational Theories for the Development of Independence in the Conditions of Destruction by Yulia N. Koreshnikova, Pavel S. Sorokin

“…An increasing number of cases have revealed that previously stable systems have shown attitudes towards unstable ones, not only generating risks, but also showing opportunities for manifestation in the manifestation of new communities and manifestations of action. …”
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Robust Stabilization Control Based on Guardian Maps Theory for a Longitudinal Model of Hypersonic Vehicle by Yanbin Liu, Mengying Liu, Peihua Sun

“…This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. …”
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Advanced Fractional Mathematics, Fractional Calculus, Algorithms and Artificial Intelligence with Applications in Complex Chaotic Systems by Dumitru Baleanu, Yeliz Karaca

“…Hence, complexity theory focuses on non-deterministic systems, whereas chaos theory rests on deterministic systems. …”
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Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties by Joaquin Alvarez-gallegos, Sishu Shankar Muni, Hector Gilardi-velázquez, Rıcardo Cuesta-garcía, J. L. Echenausía-monroy

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EXPONENTIAL DICHOTOMY OF DISCRETE TIME LINEAR SYSTEMS WITH MARKOVIAN JUMPS AND INDEPENDENT RANDOM PERTURBATIONS by Viorica Mariela UNGUREANU, Carmen Iuliana BĂRBĂCIORU

“…Exponential dichotomy is a type of conditional stability which involves the decomposition of the state space of the system into stable and unstable subspaces. By using the solution representations from [3], we provide two necessary and sufficient conditions for the uniform exponential dichotomy of the stochastic systems. …”
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Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System by Muhammad Marwan, Gauhar Ali, Ramla Khan

“…Moreover, this iterative scheme is injected into algorithms for a system of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. …”
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Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans by Scott A. Hadley, Lawrence K. Forbes

“…The limit cycles are analysed using Floquet theory and are found to change from stable to unstable as a solution branch is traversed.…”
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Research on a 3D Predator-Prey Evolutionary System in Real Estate Market by Yujing Yang, Wenzhe Tang

“…We arrive at conclusions that the phenomenon of chaos is harmful to private enterprises, and unstable behavior is often unfavorable. Thus, linear feedback control is applied to drive the model to a stable state when the system exhibits chaotic behaviors, achieving the goal of eliminating the negative effects to a large extent.…”
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Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization by Yan Cui, Hongjun He, Guan Sun, Chenhui Lu

“…We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. …”
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Study on the Dynamic Problems of Double-Disk Rotor System Supported by Deep Groove Ball Bearing by Yang Liu, Jiyuan Han, Siyao Zhao, Qingyu Meng, Tuo Shi, Hui Ma

“…The research shows that the VC vibration of the bearing has a great influence on the motion of the rotor system when the rotational speed is low. Moreover, reasonable control of bearing clearance can reduce the mutual impact between the bearing rolling element and the inner or outer rings of the bearing and reduce the influence of unstable bearing motion on the vibration characteristics of the rotor system. …”
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Vibration of Shaft System in the Mixed-Flow Pump Induced by the Rotor-Stator Interaction under Partial Load Conditions by Wei Li, Leilei Ji, Weidong Shi, Yulu Wang, Ling Zhou, Xiaoping Jiang

“…The research results can provide the reference and theory instruction for revealing the operating characteristic of mixed-flow pump when it operates under partial load conditions and to reduce or to prevent the deterioration of vibration of shaft system.…”
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Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function by Xiaoyan Liu, Quanxin Zhu

“…By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. …”
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Nonlinear Dynamics Induced by Coil Heat in the PMDC Motor and Control by André Cheukem, Alex Stéphane Kemnang Tsafack, Arnaud Ngonting Topy, Justin Roger Mboupda Pone

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Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis by Shruti Tomar, Naresh M. Chadha

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On Lorentz Invariant Complex Scalar Fields by Gustavo Rigolin

“…For interactions that break Lorentz invariance, we show that the present theories imply that particles and antiparticles behave differently at decaying processes, with the latter being more unstable. …”
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