Related papers: On fractional-order maps and their synchronization
We prove that if a certain entry in the map of the Hadamard-Perron theorem is $T$-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a $T$-periodic function. As an application,…
Inverse parallel schemes remain indispensable tools for computing the roots of nonlinear systems, yet their dynamical behavior can be unexpectedly rich, ranging from strong contraction to oscillatory or chaotic transients depending on the…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
We numerically investigate the stability and linear oscillatory behavior of a naturally diverging mass whose potential energy is harmonically modulated. It is known that in the Kapitza limit, i.e. when the period of modulation is much…
Koopman operator-based methods enable data-driven bilinear representations of unknown nonlinear control systems. Accurate representations often demand significantly higher dimensions than the original system, making control design…
In this paper, we study the construction of Lyapunov functions based on first order approximations. In a first part, the study of local exponential stability property of a transverse invariant manifold is considered. This part is mainly a…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…
This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…
The paper deals with the problem of the sampled data feedback stabilization for autonomous nonlinear systems. The corresponding results extend those obtained in earlier works by the same authors. The sufficient conditions we establish are…
This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
We study the dynamics of a family of continued fraction maps parametrized by the unit interval. This family contains as special instances the Gauss continued fraction map and the Fibonacci map. We determine the transfer operators of these…
We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential…
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions…
We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict…
Control Lyapunov Functions (CLF) method gives a constructive tool for stabilization of nonlinear systems. To find a CLF, many methods have been proposed in the literature, e.g. backstepping for cascaded systems and sum of squares (SOS)…
We present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language. They admit arbitrary switching systems as special cases. Using recent…