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Nonlinear Dynamical Systems
In Chap. 4 , we studied the dynamics of a single variable. Now we look at the dynamics of nonlinear...
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Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods
Linear multistep methods (LMMs) are popular time discretization schemes for solving the forward problem on differential equations. Recently, LMMs...
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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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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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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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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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Controllability of Prabhakar Fractional Dynamical Systems
In this manuscript, we focus on the investigation of controllability results in various types of Prabhakar fractional dynamical systems (FDSs). We...
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Mathematical Modeling of the State of Dynamical Multiplicatively Nonlinear Systems
The author formulates and solves, by the root-mean-square criterion, initial–boundary-value problems of the dynamics of nonlinear spatially...
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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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Several Dynamics of Dynamical Systems with the Eventual Shadowing Property
In this article, we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological...
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Optimal Parameter Estimation Techniques for Complex Nonlinear Systems
Accurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This...
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A Note on Quaternion Linear Dynamical Systems
We established conditions of stability and instability of quaternion linear dynamical systems, linear differential and linear fractional equations.
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Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method
AbstractThe auxiliary systems method in other words the method of two-dimensional comparison systems plays an essential role in the nonlocal...
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Algorithms for Robust Inversion of Dynamical Systems
AbstractA new methodology for solving inverse dynamics problem is developed. The methodology is based on using a mathematical model of a dynamical...
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One-dimensional monotone nonautonomous dynamical systems
This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous (cocycle) dynamical systems. A description of the...
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Two-Dimensional Quadratic Nonlinear Systems Volume I: Univariate Vector Fields
This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for...
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Traveling Wave Solutions for Nonlinear Reaction-Diffusion Equations as Dynamical Systems Problems
AbstractIn this paper we present a review of the traveling wave solutions (tws) analysis associated with different families of nonlinear...
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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 Variational Principle for the Packing Entropy of Nonautonomous Dynamical Systems
Let ( X, ϕ ) be a nonautonomous dynamical system. In this paper, we introduce the notions of packing topological entropy and measure-theoretical upper...
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Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application
The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytic Hamiltonian systems via the differential...