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Optimal Linear Response for Markov Hilbert–Schmidt Integral Operators and Stochastic Dynamical Systems
We consider optimal control problems for discrete-time random dynamical systems, finding unique perturbations that provoke maximal responses of...
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On Uniform Dichotomies for the Growth Rates of Linear Discrete-time Dynamical Systems in Banach Spaces
The aim of the present paper is to give some characterizations for the growth rates of linear discrete-time dynamical systems in Banach spaces. More...
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Invariants of Seventh-Order Homogeneous Dynamical Systems with Dissipation
AbstractNew cases of integrable seventh-order dynamical systems that are homogeneous with respect to some of the variables are presented, in which a...
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Multiplicity of positive periodic solutions to third-order variable coefficients singular dynamical systems
In this paper, by applying a nonlinear alternative principle of Leray–Schauder and Guo–Krasnosel’skii fixed point theorem on compression and...
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The Stability of Continuous-Discrete Dynamical Systems under Fast Switching
AbstractThe paper considers the problem of the influence of switching moments on the stability of the equilibrium points of nonlinear...
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From finite vector field data to combinatorial dynamical systems in the sense of Forman
We introduce a three-step method to construct on a simplicial complex a combinatorial dynamical system in the sense of Forman from vector field data...
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Composition Method for Semi-linear Parabolic Systems
An iteration method for constructing a solution to the Cauchy problem for parabolic systems with non-linear potential (reaction–diffusion) is...
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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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Discrete Dynamical Systems
So far, we have discussed the dynamics of continuous systems. An evolutionary process may also be expressed mathematically as discrete steps in time....
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Qualitative Research in the Poincaré Disk of One Family of Dynamical Systems
In this paper, we discuss a wide family of dynamical systems whose characteristic feature is a polynomial right-hand side containing coprime forms of...
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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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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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Dynamical low-rank approximation of the Vlasov–Poisson equation with piecewise linear spatial boundary
Dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov–Poisson equations is based on separation of space and velocity...
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Three-Phase Dynamical Systems and Their Applications to Monitoring for the Development of Hydrocarbon Fields
AbstractThe behavior and properties of solutions to three-phase quadratic polynomial dynamical systems on the phase plane of variables and time are...
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Chaos in One-dimensional Piecewise Smooth Dynamical Systems
In this paper, we study the family of one-dimensional piecewise smooth dynamical systems in which two classic theorems are still permanent. One of...
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Third Order Dynamical Systems for the Sum of Two Generalized Monotone Operators
In this paper, we propose and analyze a third-order dynamical system for finding zeros of the sum of two generalized operators in a Hilbert space
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Dynamical Systems
The qualitative features of the system depend on how many of the a𝑖 are negative. If all of them are, then the origin is an attractor (Fig. 11.1).
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Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs
This paper extends interpolatory model reduction to systems with (up to) quadratic-bilinear dynamics and quadratic-bilinear outputs. These systems...
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Data-Driven Modeling of Linear Dynamical Systems with Quadratic Output in the AAA Framework
We extend the Adaptive Antoulas-Anderson (
AAA ) algorithm to develop a data-driven modeling framework for linear systems with quadratic output (LQO )....
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Bohr chaoticity of topological dynamical systems
We introduce the notion of Bohr chaoticity, which is a topological invariant for topological dynamical systems, and which means that the system is...