Uniform Exponential Stability of Discrete Evolution Families on Space of p-Periodic Sequences by Yongfang Wang, Akbar Zada, Nisar Ahmad, Dhaou Lassoued, Tongxing Li

“…We prove that the discrete system ζn+1=Anζn is uniformly exponentially stable if and only if the unique solution of the Cauchy problem ζn+1=Anζn+eiθn+1zn+1,  n∈Z+, ζ0=0, is bounded for any real number θ and any p-periodic sequence z(n) with z(0)=0. …”
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Period-doubling bifurcation and Neimark-Sacker bifurcation of a discrete predator-prey model with Allee effect and cannibalism by Zhuo Ba, Xianyi Li

“…The outcome of the study reveals that this discrete system undergoes various bifurcations including period-doubling bifurcation and Neimark-Sacker bifurcation.…”
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A Two-Dimensional port-Hamiltonian Model for Coupled Heat Transfer by Jens Jäschke, Matthias Ehrhardt, Michael Günther, Birgit Jacob

“…Finally, we apply a simple spatial discretization to the system to investigate the properties of the resulting finite-dimensional port-Hamiltonian system and to determine whether the order of coupling and discretization affect the resulting semi-discrete system.…”
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Preconditioning harmonic unsteady potential flow calculations by Laird, A, Giles, M

“…Both theory and numerical results show that for a model 1D Helmholtz test problem the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. …”

Approximate solutions to the Allen–Cahn equation using rational radial basis functions method by M. Shiralizadeh, A. Alipanah, M. Mohammadi

“…Then we apply an explicit, fourth-order Runge–Kutta method to advance the resulting semi-discrete system in time. It is well known that the A.C equation has a nonlinear stability feature, meaning that the free-energy functional is reduced by time. …”
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An Adaptive in Space, Stabilized Finite Element Method via Residual Minimization for Linear and Nonlinear Unsteady Advection–Diffusion–Reaction Equations by Juan F. Giraldo, Victor M. Calo

“…We propose a residual minimization strategy that uses an ad-hoc modified discrete system that couples a time-marching schema and a semi-discrete discontinuous Galerkin formulation in space. …”
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The dynamics of synchronization of two-stage van der Pol generator by Valery V. Zaitsev, Alexander V. Karlov

“…The model was developed on the basis of the principle of compliance within the framework of the method of slowly changing amplitudes of characteristics of a discrete system with characteristics of an analog prototype. …”
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A Novel Discrete-Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population by S. Vinoth, R. Sivasamy, K. Sathiyanathan, B. Unyong, R. Vadivel, Nallappan Gunasekaran

“…The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. …”
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Fault Detection for Wireless Network Control Systems with Stochastic Uncertainties and Time Delays by Jie Zhang, Pengfei Guo, Ming Lyu, Hamid Reza Karimi, Yuming Bo

“…Then, by constructing proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the fault detection observer for the discrete system, and observer gain is also derived by solving linear matrix inequalities. …”
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Bifurcations of a three-species prey-predator system with scavenger by Abdul Qadeer Khan, Syed Saqlain Kazmi, Turki D. Alharbi

“…More specifically, it is proved that for all parameters, the discrete system has trivial and boundary fixed points; two more boundary fixed points, and an interior fixed point under a certain model's parametric restriction(s). …”
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5D Nonlinear Dynamic Evolutionary System in Real Estate Market by Jingyuan Zhang

“…The corresponding discrete system is simulated, and the simulation results about Lyapunov spectrum, bifurcation diagram, sequence diagram, and phase diagram are given. …”
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Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems by Hongyan Zang, Mengdan Tai, Xinyuan Wei

“…First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense of Li–Yorke, and the corresponding chaos criterion theorem is proposed. …”
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About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma by M. De la Sen

“…This paper formulates an “ad hoc” robust version under parametrical disturbances of the discrete version of the Kalman-Yakubovich-Popov Lemma for a class of positive hybrid dynamic linear systems which consist of a continuous-time system coupled with a discrete-time or a digital one. An extended discrete system, whose state vector contains both the digital one and the discretization of the continuous-time one at sampling instants, is a key analysis element in the formulation. …”
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Some Bifurcations of Codimensions 1 and 2 in a Discrete Predator–Prey Model with Non-Linear Harvesting by Ming Liu, Linyi Ma, Dongpo Hu

“…The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. …”
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A Discrete Numerical Scheme of Modified Leslie-Gower With Harvesting Model by Riski Nur Istiqomah Dinnullah, Trija Fayeldi

“…It is shown that the numerical simulations not only illustrate the results, but also show the rich dynamics behaviors of the discrete system.…”
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Natural Oscillations of Plate-Beam Floor Fragment of Buildings by P.W. Aliawdin, Yu.A. Muzychkin

“…For the initial model, as for a discrete system, modeling of natural and harmonic oscillations on the basis of the finite element method is executed. …”
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Displacements of the Levitation Systems in the Vehicle Hyperloop by Jerzy Kisilowski, Rafał Kowalik

“…The paper will present a mathematical model for the guideway as a continuous system, followed by a moving force coming from the capsule and the capsule as a discrete system. The theoretical problem selected for analysis comes from a group of technical problems, which solve the dynamics of systems subjected to moving loads. …”
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The role of smoothing effect in some dispersive equations by Grande Izquierdo, Ricardo.

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Certification Disclosure and Informational Efficiency: A Case for Ordered Ranking of Levels. by Guerra, G

“…The predicted disclosure is consistent with real life observations of certification disclosure as found in debt ratings (notches) and hotels listings (using a discrete system of stars). The model is robust enough to explain the results of previous models. …”

Certification disclosure and informational efficiency: a case for ordered ranking of levels by Guerra, G

“…The predicted disclosure is consistent with real life observations of certification disclosure as found in debt rating (notches) and hotels listings (using a discrete system of stars). The model is robust enough to explain the results of previous models. …”