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Discrete Dynamical Systems in Economics: Two Seminal Models and Their Developments
This survey paper starts from two famous discrete-time dynamic models in economics, namely the Cobweb model to describe price dynamics and the...
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Algebraic Dynamical Systems in Machine Learning
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an...
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Dynamical Systems
The motion of the planets and moons in our solar system is a dynamical system that has been studied throughout recorded history. Although some of the...
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Sensitivity Analysis of Random Linear Dynamical Models Using System Norms
We consider linear dynamical systems with a single output, where the systems include random parameters to perform an uncertainty quantification....
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Continuous Dynamical Systems
DynamicsDynamics is a time-evolutionary process. It may be deterministic or stochastic. Long-term predictions of some systems often become...
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On Optimal Control Problems for Dynamical Systems in Real Time
This paper is a review of the results on the real-time optimal control problem for linear systems obtained by the Minsk school by mathematical...
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Efficient Analytical Algorithms to Study Fokas Dynamical Models Involving M-truncated Derivative
The dynamical behaviour of the (4+1)-dimensional fractional Fokas equation is investigated in this paper. The modified auxiliary equation method and...
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Slow-Fast Dynamical Systems with a Load Variation
We analyze a category of slow-fast dynamical systems that exhibit complex bifurcations as the dynamic parameter, representing the load on the system,...
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Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically,...
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Topological Dynamic Consistency of Numerical Methods for Dynamical Models in Biosciences
Qualitative analysis of dynamical systems modelling biological processes makes a valuable contribution to understanding these processes and...
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Networked Dynamical System Models
In this chapter, we first introduce several commonly used networked dynamical models. We then introduce examples of the considered networked...
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Global Attractors for a Class of Discrete Dynamical Systems
In this paper, we study the existence of global attractors for a class of discrete dynamical systems naturally originated from impulsive dynamical...
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Forward invariant set preservation in discrete dynamical systems and numerical schemes for ODEs: application in biosciences
We present two results on the analysis of discrete dynamical systems and finite difference discretizations of continuous dynamical systems, which...
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Observability of Time-Varying Fractional Dynamical Systems with Caputo Fractional Derivative
Modeling dynamical systems with real-life data having time-dependent disturbances is better captured with time-varying systems. The qualitative...
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Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition...
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Dynamical Systems
Dynamical systems are mathematical models concerning variables that change depending on time. In this chapter, we consider a system represented by a...
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Dynamical Systems on Graph Limits and Their Symmetries
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than...
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Quadratic points on dynamical modular curves
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This...
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Introduction to Dynamical Systems
This chapter introduces some basic terminology. First, we define a dynamical system and give several examples, including symbolic dynamics. Then we...
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Dynamical Survival Analysis for Epidemic Modeling
This chapter describes the dynamical survival analysis (DSA) method for modeling infectious diseases. This method provides a powerful framework for...