Continuous approximations of a class of piece-wise continuous systems

2014/02/27 by Marius‐F. Danca, Danca, Marius-F. · 1 citation
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1402.6816

openalex publication_date 2014/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise functions can be locally or globally approximated. The approximation results can be used to model piece-wise continuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for diffrential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.

Citations

• Linear Models of Dissipation whose Q is almost Frequency Independent--II

Cited by

• Unifying Cosmic Epochs via Quantum-Corrected Expansion with Brane-World Parallels

Related

• Lyapunov exponents of a class of piecewise continuous systems of\n fractional order
• Chaotic behavior of a class of discontinuous dynamical systems of\n fractional-order
• Rational approximations, multidimensional continued fractions and lattice reduction
• Numerical Models for the Simulation of the Fractional-Order Control Systems
• Modelling and analysis of fractional-order regulated systems in the state space