Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems by Min Wu, Zhengfeng Yang, Wang Lin

“…We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. …”
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Integrity Design for Networked Control Systems with Actuator Failures and Data Packet Dropouts by Xiaomei Qi, Jason Gu

“…After introducing the matrix of actuator failure, the closed-loop NCS is developed, which can be viewed as asynchronous dynamical systems (ADSs). Then, the sufficiency of exponential stability for the NCS is obtained based on the theory of ADSs. …”
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On the structural stability of a simple cosmological model in R + αR2 theory of gravity by Orest Hrycyna

“…The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann–Robertson–Walker metric is employed to formulate the dynamics in both the Jordan frame and the conformally transformed Einstein frame. …”
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Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators by Azhar Hussain, Ahsan Ali, Vahid Parvaneh, Hassen Aydi

“…To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.…”
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Active stabilization of a chaotic urban system by Günter Haag, Tilo Hagel, Timm Sigg

“…A new method to stabilize dynamical systems by forcing the system variables into the desired unstable stationary point is proposed. …”
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Triopoly Cournot–Bertrand Game Based on Fractional Bounded Rationality: Static and Dynamic Investigations by Mahmoud Awad, Mohamed Abouhawwash, S. S. Askar, H. N. Agiza

“…Finally, we present a numerical study of the dynamical system, demonstrating that a small degree of memory enhances system stability.…”
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Solving Hyperchaotic Systems Using the Spectral Relaxation Method by S. S. Motsa, P. G. Dlamini, M. Khumalo

“…A new multistage numerical method based on blending a Gauss-Siedel relaxation method and Chebyshev pseudospectral method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. …”
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Approximate Prediction-Based Control Method for Nonlinear Oscillatory Systems with Applications to Chaotic Systems by Thiago P. Chagas, Pierre-Alexandre Bliman, Karl H. Kienitz

“…The approximate Prediction-Based Control method (aPBC) is the continuous-time version of the well-known Prediction-Based Chaos Control method applied to stabilize periodic orbits of nonlinear dynamical systems. The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. …”
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A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems by Mufutau Ajani Rufai, Ali Shokri, Ezekiel Olaoluwa Omole

“…This research is significant because it has numerous applications to real-life phenomena such as chaotic dynamical systems, almost periodic problems, and duffing equations. …”
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IMU Optimal Rotation Rates by Patrick Grates

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A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications by Baltazar Aguirre-Hernández, Raúl Villafuerte-Segura, Alberto Luviano-Juárez, Carlos Arturo Loredo-Villalobos, Edgar Cristian Díaz-González

“…This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. …”
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Discovering and Characterizing Hidden Variables Using a Novel Neural Network Architecture: LO-Net by Soumi Ray, Tim Oates

“…Experiments show the utility of the proposed approach using discrete time dynamical systems, in which some of the state variables are hidden, and sensor data obtained from the camera of a mobile robot, in which the sizes and locations of objects in the visual field are observed but their sizes and locations (distances) in the three-dimensional world are not. …”
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Analysis and Enhancements of a Prolific Macroscopic Model of Epilepsy by Christopher Fietkiewicz, Kenneth A. Loparo

“…Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. …”
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Dynamics Analysis and Intermittent Energy Feedback Control of m-HR Neuron Model under Electromagnetic Induction by Jiankui Peng, Suoping Li

“…Meanwhile, it should be emphasized that the intermittent control scheme has a wider range of regulation and robustness, which can be applied to other dynamical systems to obtain the desired oscillation modes. …”
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Recurrences Reveal Shared Causal Drivers of Complex Time Series by William Gilpin

“…Combining the theory of skew-product dynamical systems with topological data analysis, we show that simultaneous recurrence events across multiple time series reveal the structure of their shared unobserved driving signal. …”
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Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control by Guangyao Tang, Jin Yang, Sanyi Tang

“…Spiking neuron models which exhibit rich dynamics are usually defined by hybrid dynamical systems. It is revealed that mathematical analysis of these models has important significance. …”
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Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems by Mauricio J. del Razo, Luigi Delle Site

“…As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.…”
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Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt by S. P. Chen, Y. H. Qian

“…The improved method is described in detail by analyzing the four-dimensional nonlinear dynamical systems whose Jacobian matrices evaluated at an equilibrium point contain three different cases, that are, (i) two pairs of pure imaginary eigenvalues, (ii) one nonsemisimple double zero and a pair of pure imaginary eigenvalues, and (iii) two nonsemisimple double zero eigenvalues. …”
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Hidden Attractors in Chaotic Systems with Nonlinear Functions by Safara Bibi, Juan Hugo García López, Rider Jaimes-reategui, Hafiz Muhammad Zeeshan, Guillermo Huerta-cuellar

“…In the present work, an interesting mini-review of hidden attractors in dynamical systems with associated nonlinear functions is carried out. …”
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Neural Network and Hybrid Methods in Aircraft Modeling, Identification, and Control Problems by Gaurav Dhiman, Andrew Yu. Tiumentsev, Yury V. Tiumentsev

“…That is, it is required to solve also the identification problem for dynamical systems. We propose an approach to solving the above-mentioned problems based on artificial neural networks (ANNs) and hybrid technologies. …”
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