Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis by Firaol Asfaw Wodajo, Temesgen Tibebu Mekonnen

“…We proved that the solution of the considered dynamical system is positive and bounded. The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. …”
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Analysis of Prey-Predator Scheme in Conjunction with Help and Gestation Delay by M. Mukherjee, D. Pal, S. K. Mahato, Ebenezer Bonyah, Ali Akbar Shaikh

“…This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. …”
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ANALYTICAL SYNTHESIS OF FORCED PULSE ELECTRONIC DRIVE CONTROL OF A TRACKING SYSTEM by A. S. Abufanas, A. A. Lobaty, Y. F. Yacina

“…The problem of analytical synthesis of a control signal by a linear dynamical system is considered. As an optimization criterion, it is proposed to consider the transition time of the system from the initial state to a given final state. …”
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Quantum-Ordering Ambiguities in Weak Chern—Simons 4D Gravity and Metastability of the Condensate-Induced Inflation by Panagiotis Dorlis, Nick E. Mavromatos, Sotirios-Neilos Vlachos

“…On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. …”
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A proximal policy optimization based deep reinforcement learning framework for tracking control of a flexible robotic manipulator by Joshi Kumar V, Vinodh Kumar Elumalai

“…Identifying the optimal hyper-parameters of DRL using the grid search method, we exploit the capability of CNN in actor-critic architecture to extract the spatial dependencies in the state sequences of the dynamical system and boost the DRL performance. To improve the convergence of the proposed DRL algorithm, this study adopts the Lyapunov based reward shaping technique. …”
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A quantitative analysis of Koopman operator methods for system identification and predictions by Zhang, Christophe, Zuazua, Enrique

“…We give convergence and cost estimates for a data-driven system identification method: given an unknown dynamical system, the aim is to recover its vector field and its flow from trajectory data. …”
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Adaptive Kalman Filtering: Measurement and Process Noise Covariance Estimation Using Kalman Smoothing by Theresa Kruse, Thomas Griebel, Knut Graichen

“…For higher-dimensional problems, the convergence can be tested simulatively for the specific dynamical system. A detailed evaluation of various simulation scenarios is presented, demonstrating the accuracy and robustness of the proposed method.…”
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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

“…The study of dynamical systems is based on the solution of differential equations that may exhibit various behaviors, such as fixed points, limit cycles, periodic, quasi-periodic attractors, chaotic behavior, and coexistence of attractors, to name a few. …”
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Uncovering Deterministic Behavior of Black Hole IGR J17091–3624: A Twin of GRS 1915+105 by Anindya Guria, Banibrata Mukhopadhyay

“…We find signs of determinism in IGR J17091–3624, thus supporting the hypothesis of it being similar to GRS 1915+105, even as a dynamical system. Our findings not only shed light on the complex nature of IGR J17091–3624 but also pave the way for future research employing noise-reduction techniques to analyze nonlinearity in observed dynamical systems.…”
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A statistical approach to the use of control entropy identifies differences in constraints of gait in highly trained versus untrained runners by Rana D. Parshad, Stephen J. McGregor, Michael A. Busa, Joseph D. Skufca, Erik Bollt

“…Control entropy (CE) is a complexity analysis suitable fordynamic, non-stationary conditions which allows the inference of the control effort of a dynamical system generating the signal [4]. These characteristics make CE a highly relevant time varying quantity relevant to the dynamic physiological responses associated with running. …”
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Exploring optimal control strategies in a nonlinear fractional bi-susceptible model for Covid-19 dynamics using Atangana-Baleanu derivative by Azhar Iqbal Kashif Butt, Waheed Ahmad, Hafiz Ghulam Rabbani, Muhammad Rafiq, Shehbaz Ahmad, Naeed Ahmad, Saira Malik

“…The asymptotic stabilities of the dynamical system at its two main equilibrium states are determined by the essential conditions imposed on the threshold parameter. …”
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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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Advanced Fractional Mathematics, Fractional Calculus, Algorithms and Artificial Intelligence with Applications in Complex Chaotic Systems by Dumitru Baleanu, Yeliz Karaca

“…Chaos, comprehended characteristically, is the mathematical property of a dynamical system which is a deterministic mathematical model in which time can be either continuous or discrete as a variable. …”
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Designing of a Personality Based Emotional Decision Model for Generating Various Emotional Behavior of Social Robots by Ho Seok Ahn

“…The personality-based emotional decision model is designed with four linear dynamics, viz. reactive dynamic system, internal dynamic system, emotional dynamic system, and behavior dynamic system. …”
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Oral English Development of EFL Learners from the Perspective of Complexity Dynamic Theory by Qiang Dou, Guohua Li, Yuan Tang

“…The purpose of this paper is to explore the learning situation of oral English of EFL learners from the perspective of the complex dynamic system theory and provide some new learning methods and suggestions for EFL learners’ oral English learning based on the research of complex dynamic system theory. …”
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The Stability Criteria with Compound Matrices by Yazhuo Zhang, Baodong Zheng

“…The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.…”
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Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent by Miguel Alfaro, Guillermo Fuertes, Manuel Vargas, Juan Sepúlveda, Matias Veloso-Poblete

“…The theory of the nonlinear dynamic systems indicates the capacity of making good-quality predictions of series coming from dynamic systems with chaotic behavior up to a temporal horizon determined by the inverse of the major Lyapunov exponent. …”
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Family of Bistable Attractors Contained in an Unstable Dissipative Switching System Associated to a SNLF by J. L. Echenausía-Monroy, J. H. García-López, R. Jaimes-Reátegui, D. López-Mancilla, G. Huerta-Cuellar

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Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review by Matthew B. Wagner, Amir Younan, Paul Allaire, Randy Cogill

“…The focus of this literature survey and review is model reduction methods and their application to rotor dynamic systems. Rotor dynamic systems require careful consideration in their dynamic models as they include unsymmetric stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. …”
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Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems by Andrzej Stefanski, Tomasz kapitaniak

“…We describe the method of estimation of the largest Lyapunov exponent of nonsmooth dynamical systems using the properties of chaos synchronization. …”
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