Application of the Natural Decomposition Method to Strongly Coupled Partial Differential Equations: The Gray-Scott Model. by Nsingwire, Godwin

“…Numerical techniques, such as the Newton-Raphson method, were integrated to handle the nonlinear algebraic equations, particularly those involving the term𝑢𝑣2. …”
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Evolutionary distributions in adaptive space by Yosef Cohen

“…We argue that in evolutionary context, predator prey models with predator saturation make less sense than in ecological models. Also, with ED, the dynamics of population genetics may be reduced to an algebraic problem. …”
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Vector Bond Graph Method of Kineto- static Analysis for Hybrid Driving Five Linkage Mechanism by Wang Zhongshuang, Wang Xifeng

“…According to the adjacency relationship of the components of hybrid driving five bar linkage mechanism,the vector bond graph model of hybrid driving five bar linkage is established by assembling the vector bond graph model of planar moving rigid body,revolute joint and translational joint. For the algebraic difficulties brought by differential causality and nonlinear junction structure in automatic modeling and dynamics analysis of this kind mechanism,the effective bond graph augment method is proposed. …”
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Couple-Group Consensus: A Class of Delayed Heterogeneous Multiagent Systems in Competitive Networks by Lianghao Ji, Yue Zhang, Yiliu Jiang

“…In distinction to the existing works, a novel distributed coordination control protocol is proposed which is not only on the foundation of the competitive interaction between the agents but also has no virtual velocity estimation in the first-order dynamics. Furthermore, without the restrictive assumptions existing commonly in the related works, several sufficient algebraic criteria are established for the heterogeneous systems to realize couple-group consensus asymptotically. …”
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Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series by Erez Abrams, Michael Kasprzak, Gaurav Bhole, Tak-San Ho, Herschel Rabitz

“…Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. …”
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A Direct Eigenanalysis of Multibody System in Equilibrium by Cheng Yang, Dazhi Cao, Zhihua Zhao, Zhengru Zhang, Gexue Ren

“…The first kind Lagrange’s equation of the dynamics of multibody system is a set of differential algebraic equations, and the equations can be used to solve the equilibrium of the system. …”
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Evaluation of Cross-Coupling Decoupling in Islanded Microgrid Control with Inductor Current Feed-Forward Technique by Sunday Olayanju, Folasade Mojisola Dahunsi, Akinlolu Adediran Ponnle

“…This paper presents stepwise design and modelling of the inverter dynamics in the d-q reference frame. The systematic algebraic elimination method with inductor current feed-forward was employed for decoupling cross-coupling terms in the current and voltage loop controller design. …”
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Adaptive Fuzzy Consensus Tracking Control for Nonlinear Multiagent Systems with Time-Varying Delays and Constraints by Jie Lan, Tongyu Xu

“…This paper proposes an adaptive fuzzy distributed consensus tracking control scheme for a class of uncertain nonlinear dynamic multiagent systems (MASs) with state time-varying delays and state time-varying constraints. …”
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A Sliding Mode LCO Regulation Strategy for Dual-Parallel Underactuated UAV Systems Using Synthetic Jet Actuators by N. Ramos-Pedroza, W. MacKunis, M. Reyhanoglu

“…This difficulty is mitigated through careful algebraic manipulation in the regulation error system development, along with innovative design of the sliding surface. …”
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Theoretical and numerical study of profit in agricultural sector model using wavelet method by Yeshwanth R., Kumbinarasaiah S.

“…The operational matrices are used to simplify fractional differential equations to an algebraic system of equations. Finally, we graphically depict the results and offer empirical support for our theoretical conclusions through graphic representations. …”
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Voltage Stability Analysis of Front-End Speed Controlled Wind Turbine Integrated into Regional Power Grid Based on Bifurcation Theory by Kaide Ren, Hongwei Li, Shuaibing Li, Haiying Dong

“…Firstly, differential-algebraic equations (DAEs) describing the dynamic characteristics of the wind turbine are given and the mathematical model of the system includes FSCWT is established. …”
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Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source by V. S. Malyar, A. V. Malyar

“…The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. …”
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Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control by J. Humberto Pérez-Cruz, Pedro A. Tamayo-Meza, Maricela Figueroa, Ramón Silva-Ortigoza, Mario Ponce-Silva, R. Rivera-Blas, Mario Aldape-Pérez

“…Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. …”
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On Refinements of Multidimensional Inequalities of Hardy-Type via Superquadratic and Subquadratic Functions by M. Zakarya, Ghada AlNemer, H. A. Abd El-Hamid, Roqia Butush, H. M. Rezk

“…The performance of the superquadratic functions is reliable and effective to obtain new dynamic inequalities on time scales. By utilizing special kernels, we also acquire numerous examples and implementations of the related inequalities.…”
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Syntheses of differential games and pseudo-Riccati equations by Yuncheng You

“…For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). …”
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Transient Response of Multiple Interface Cracks in Fine-Grained Coating Composite Structures under Impact Loading by Shuaishuai Hu, Junlin Li

“…Then, the expression of the dynamic energy release rate is given with the help of the dynamic intensity factors of electric displacement and stress obtained. …”
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Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems by Hong Shi, Guangming Xie

“…Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. …”
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Efficient Convex Optimization of Reentry Trajectory via the Chebyshev Pseudospectral Method by Chun-Mei Yu, Dang-Jun Zhao, Ye Yang

“…The Chebyshev-Gauss Legend (CGL) node points are used to transcribe the original dynamic constraint into algebraic equality constraint; therefore, a nonlinear programming (NLP) problem is concave and time-consuming to be solved. …”
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Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity by Hongmei Wu, Zhiying Ou

“…Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. …”
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Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness by Dongli Wu, Hao Zhang, Yunping Liu, Weihua Fang, Yan Wang

“…The trajectory planning of UAV with nonholonomic constraints is usually taken as differential algebraic equation to solve the optimal control problem of functional extremum under the condition of inequality constraints. …”
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