Large-Eddy Simulation of the Flow Past a Circular Cylinder at Re = 130,000: Effects of Numerical Platforms and Single- and Double-Precision Arithmetic by Dmitry A. Lysenko

“…The reconstructed attractors of the dynamic systems in phase space are limited by an ellipsoid.…”
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Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion by Lingzhi Huang, Zhichun Yang

“…By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. …”
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Mutation and Chaos in Nonlinear Models of Heredity by Nasir Ganikhodjaev, Mansoor Saburov, Ashraf Mohamed Nawi

“…We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. …”
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Double Weak Hopf Quiver and Its Path Coalgebra by Muhammad Naseer Khan, Munir Ahmed, Muhammad Arshad, Waleed Almutiry, Rashad A. R. Bantan, Mohammed Elgarhy

“…These structures are important in the physics for dynamic systems.…”
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Operating with External Arguments of Douady and Hubbard by G. Pastor, M. Romera, G. Alvarez, J. Nunez, D. Arroyo, F. Montoya

“…The external arguments of the external rays theory of Douady and Hubbard is a valuable tool in order to analyze the Mandelbrot set, a typical case of discrete dynamical system used to study nonlinear phenomena. We suggest here a general method for the calculation of the external arguments of external rays landing at the hyperbolic components root points of the Mandelbrot set. …”
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Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator by Nguyen Dinh Binh

“…We prove the regularity and exponential growth of a pullback attractor in the space S02(Ω)∩L2p−2(Ω) for the nonautonomous dynamical system associated to the problem. The obtained results seem to be optimal and, in particular, improve and extend some recent results on pullback attractors for reaction-diffusion equations in bounded domains.…”
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Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control by Xiaobing Zhou, Lianglin Xiong, Weiwei Cai, Xiaomei Cai

“…The essential conditions are derived under which the synchronization or antisynchronization error dynamical system could be equivalent to a passive system and be globally asymptotically stabilized at a zero equilibrium point via smooth state feedback. …”
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A novel approach to Lyapunov stability of Caputo fractional dynamic equations on time scale using a new generalized derivative by Michael Precious Ineh, Edet Peter Akpan, Hossam A. Nabwey

“…The results presented in this work contributed to the broader understanding of fractional calculus on time scales, enriching the theoretical foundation of dynamic systems analysis. Illustrative examples were included to demonstrate the effectiveness, relevance, and practical applicability of the established stability and asymptotic stability results. …”
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Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications by Jiang Zhu, Dongmei Liu

“…By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.…”
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Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control by Chunjin Wei, Lansun Chen

“…By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. …”
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Basic stage structure measure valued evolutionary game model by John Cleveland

“…A general model of this basic stage structure is formulated as a dynamical system on the state space of finite signed measures.Nonnegativity, well-posedness and uniform eventual boundedness are established under biologically natural conditions on the rates. …”
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Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems by Chenhui Wang

“…The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. …”
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New Exact Solutions, Dynamical and Chaotic Behaviors for the Fourth-Order Nonlinear Generalized Boussinesq Water Wave Equation by Cheng Chen, Zuolei Wang

“…Then, the fourth-order nonlinear generalized Boussinesq water wave equation is transformed into the planer dynamical system under traveling wave transformation. We also investigate the dynamical behaviors and chaotic behaviors of the considered equation. …”
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Nonlinear Dynamic Analysis and Synchronization of Four-Dimensional Lorenz-Stenflo System and Its Circuit Experimental Implementation by Cheng-Hsiung Yang, Cheng-Lin Wu

“…In this paper, first a new nonlinear chaotic dynamical system had be design, analyze and build circuit. …”
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Cosmological Dynamics of a Hybrid Chameleon Scenario by Kourosh Nozari, Narges Rashidi

“…By introducing an effective potential, we study the dependence of the effective potential's minimum and hybrid chameleon field's masses on the local matter density. In a dynamical system technique, we analyze the phase space of this two-field chameleon model, find its fixed points and study their stability. …”
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Physiologically Based Structure of Mean Residence Time by Mária Durišová

“…Therefore, tools from the theory of linear dynamic systems were used for the structural identification of MRT in this study. …”
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A Note on the Observability of Temporal Boolean Control Network by Wenping Shi, Bo Wu, Jing Han

“…Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. …”
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Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response by C. Gokila, M. Sambath, K. Balachandran, Yong-Ki Ma

“…We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. …”
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Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators by Bo Qin, Huilin Shang, Huimin Jiang

“…First, static bifurcation of the dynamical system is discussed. Then, via analyzing the effect of the external excitation on the periodic solutions under primary resonance, it is found that the change of the excitation frequency may lead to bistability and safe jump. …”
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Solvency Evaluation Model of Insurance Company Based on Stochastic Differential Equation by Kai Wang, Ling Zhu

“…In this paper, from the perspective of capital flow, the insurance company’s capital flow is regarded as a dynamic system, the stochastic differential equations model is established to describe its flow characteristics, and the existence of positive equilibrium point of the system is proved, as well as the conditions of stability at equilibrium point, that is, the requirements of the insurance company’s solvency. …”
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