Generalization of neural network models for complex network dynamics by Vaiva Vasiliauskaite, Nino Antulov-Fantulin

“…Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems, especially in complex systems that lack explicit first principles. …”
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Modeling and analysis of a simple manufacturing-oriented multi-agent system by P. Levi, M. Schanz, V. Avrutin

“…In order to develop appropriate tools for this task, the dynamic behaviour of the system is investigated using concepts and methods of synergetics and the theory of nonlinear dynamical systems.…”
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Adapting physics-informed neural networks to improve ODE optimization in mosquito population dynamics. by Dinh Viet Cuong, Branislava Lalić, Mina Petrić, Nguyen Thanh Binh, Mark Roantree

“…The integration of physics principles enables the method to require less data while maintaining the robustness of deep learning in modelling complex dynamical systems. However, current PINN frameworks are not sufficiently mature for real-world ODE systems, especially those with extreme multi-scale behavior such as mosquito population dynamical modelling. …”
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Holling-Tanner Predator-Prey Model with State-Dependent Feedback Control by Jin Yang, Guangyao Tang, Sanyi Tang

“…In this paper, we propose a novel Holling-Tanner model with impulsive control and then provide a detailed qualitative analysis by using theories of impulsive dynamical systems. The Poincaré map is first constructed based on the phase portraits of the model. …”
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Marker and source-marker reprogramming of Most Permissive Boolean networks and ensembles with BoNesis by Paulevé, Loïc

“…Boolean networks (BNs) are discrete dynamical systems with applications to the modeling of cellular behaviors. …”
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Performance Enhancement of MRAC via Generalized Dynamic Inversion by Alharith Mahmoud, Abdulrahman H. Bajodah

“…Model Reference Adaptive Control (MRAC) guarantees closed loop stability and desired steady state performance of dynamical systems without undue dependence upon their mathematical models. …”
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Quantized Dissipative Observer-Based Output Feedback Control for a Class of Markovian Descriptor Jump Systems with Communication Delay by Muhammad Shamrooz Aslam, Xisheng Dai

“…The descriptor systems are presented as Markovian jump systems which give a more realistic presentation for a variety of nonlinear dynamical systems than conventional state-space representation. …”
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Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations by Zhao Li, Peng Li, Tianyong Han

“…Then, the traveling wave solutions of the fractional generalized Hirota–Satsuma coupled KdV equations corresponding to phase orbits are easily obtained by applying the method of planar dynamical systems; these solutions include not only the bell solitary wave solutions, kink solitary wave solutions, anti-kink solitary wave solutions, and periodic wave solutions but also Jacobian elliptic function solutions. …”
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Diagenetic Self-Organization and Stochastic Resonance in a Model of Limestone-Marl Sequences by Ivan L’Heureux

“…The model exhibits interesting features typical of nonlinear dynamical systems: (i) the existence of self-organized oscillating patterns between a calcite-rich mode (“limestone”) and a calcite-poor one (“marl”) for fixed environmental conditions and (ii) bistability between these two modes. …”
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A Fully Operational Framework for Handling Cellular Automata Templates by Mauricio Verardo, Pedro P. B. de Oliveira

“…Cellular automata are fully discrete, computational, or dynamical systems, characterised by a local, totally decentralised action. …”
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Dynamical Models of Tuberculosis and Their Applications by Carlos Castillo-Chavez, Baojun Song

“…Most recently developed models not only payattention to simulations but also take care of dynamical analysisusing modern knowledge of dynamical systems. Questions addressed bythese models mainly concentrate on TB control strategies, optimalvaccination policies, approaches toward the elimination of TB in theU.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responsesof the immune system, impacts of demography, the role of publictransportation systems, and the impact of contact patterns. …”
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The Gauge Integral Theory in HOL4 by Zhiping Shi, Weiqing Gu, Xiaojuan Li, Yong Guan, Shiwei Ye, Jie Zhang, Hongxing Wei

“…The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. …”
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A New Fractional-Order Map with Infinite Number of Equilibria and Its Encryption Application by Ahlem Gasri, Amina-Aicha Khennaoui, Adel Ouannas, Giuseppe Grassi, Apostolos Iatropoulos, Lazaros Moysis, Christos Volos

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Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles by Yaoyao Wang, Jiawang Chen, Linyi Gu

“…Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time.…”
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A New Mathematical Modeling with Optimal Control Strategy for the Dynamics of Population of Diabetics and Its Complications with Effect of Behavioral Factors by Abdelfatah Kouidere, Abderrahim Labzai, Hanane Ferjouchia, Omar Balatif, Mostafa Rachik

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Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System by Nadjette Debbouche, Adel Ouannas, Iqbal M. Batiha, Giuseppe Grassi, Mohammed K. A. Kaabar, Hadi Jahanshahi, Ayman A. Aly, Awad M. Aljuaid

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Dynamical behavior analysis and traveling wave solution of stochastic Riemann wave equations by Jie Luo, Jiangtao Guo, Yan Shao, Guangxu Zhao, Min Jiao

“…Finally, two-dimensional planar dynamical systems and its disturbance systems are considered by using Mathematical software. …”
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Understanding Ecosystem Complexity via Application of a Process-Based State Space rather than a Potential Surface by C. Gaucherel, F. Pommereau, C. Hély

“…Ecologists still struggle to understand ecosystems, and one main method for achieving an understanding consists in computing potential surfaces based on physical dynamical systems. We argue in this conceptual paper that the foundations of this analogy between physical and ecological systems are inappropriate and aim to propose a new method that better reflects the properties of ecosystems, especially complex, historical nonergodic systems, to which physical concepts are not well suited. …”
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Global dynamics of a simple model for wild and sterile mosquitoes by Yu Ichida, Yukihiko Nakata

“…In this paper, we combine a geometric approach called the time-scale transformation and blow-up technique with the center manifold theorem to provide a complete understanding of dynamical systems near the origin. Then, the global behavior of the solution of the two-dimensional ordinary differential equation system is classified in a two-parameter plane represented by the natural death rate of mosquitoes and the sterile mosquito release rate. …”
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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

“…By using simple powerful tools of analyzing nonlinear dynamical systems like phase portraits, time traces and frequency spectrum in the MATLAB-SIMULINK environment, we showed that under certain conditions, the PMDC motor develops different behaviors so as periodic limited, and chaotic attractors, when the motor drive different form of external load torque and the windings resistance variation. …”
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