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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Transitions in intensive care: Investigating critical slowing down post extubation. by Lucinda Khalil, Sandip V George, Katherine L Brown, Samiran Ray, Simon Arridge

“…While immediate clinical utility is limited, the work marks an important first step towards using dynamical systems theory to understand the dynamics of signals measured at the bedside during intensive care.…”
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Comparing Two Strategies to Model Uncertainties in Structural Dynamics by Rubens Sampaio, Edson Cataldo

“…In the modeling of dynamical systems, uncertainties are present and they must be taken into account to improve the prediction of the models. …”
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Numerical Exploration of Kaldorian Interregional Macrodynamics: Enhanced Stability and Predominance of Period Doubling under Flexible Exchange Rates by Toichiro Asada, Christos Douskos, Vassilis Kalantonis, Panagiotis Markellos

“…The paper illustrates the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters.…”
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TIE‐GCM ROPE ‐ Dimensionality Reduction: Part I by Piyush M. Mehta, Richard J. Licata

“…The methodology uses a page out of dynamical systems theory to first reduce the order of the state using dimensionality reduction and then modeling the temporal dynamics in the reduced state space. …”
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Multi-host transmission dynamics of schistosomiasis and its optimal control by Chunxiao Ding, Zhipeng Qiu, Huaiping Zhu

“…The dynamics of the model is rigorously analyzed by using the theory of dynamical systems. The theoretical results show that the disease free equilibrium is globally asymptotically stable if $\mathcal R_0<1 and="" if="" mathcal="" r_0="">1$ the system has only one positive equilibrium. …”
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On the Optimal Control of HIV-TB Co-Infection and Improvement of Workplace Productivity by Baba Seidu, Oluwole Daniel Makinde, Ibrahim Yakubu Seini

“…The impact of these diseases on workforce productivity is studied in this paper from the viewpoint of dynamical systems. In this paper, we present a nonlinear ordinary differential equation model to study the dynamics of HIV-TB co-infection and its effect on workforce productivity. …”
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Lump-type kink wave phenomena of the space-time fractional phi-four equation by Khudhayr A. Rashedi, Musawa Yahya Almusawa, Hassan Almusawa, Tariq S. Alshammari, Adel Almarashi

“…The conformable fractional derivative played the role of improving the modeling of the complex dynamical systems. The obtained solutions, which were illustrated by giving 2D, 3D MATLAB plots and contour illustrations, were s eful in nuclear, particle physics and fluid mechanics. …”
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The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain Volatility by Lorella Fatone, Francesca Mariani, Maria Cristina Recchioni, Francesco Zirilli

“…The method proposed here for calibrating the Black-Scholes dynamics model could be extended to other science and engineering models that may be expressed in terms of stochastic dynamical systems.…”
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From the Guest Editors by Fred Brauer, Carlos Castillo-Chavez, Thomas G. Hallam, Jia Li, Jianhong Wu, Yicang Zhou

“…Hence, it is not surprising to see his shift from an outstanding contributor to the field of dynamical systems to a pioneer in the field of mathematical biology. …”
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Locally conformal symplectic manifolds by Izu Vaisman

“…L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. …”
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