Related papers: Exploring F-Sensitivity for Non-Autonomous Systems
We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…
A CF explainer identifies the minimum modifications in the input that would alter the model's output to its complement. In other words, a CF explainer computes the minimum modifications required to cross the model's decision boundary.…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…
In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous…
Let $\boldsymbol{X}=\{X_k\}_{k=0}^\infty$ be a sequence of compact metric spaces $X_{k}$ and $\boldsymbol{T}=\{T_k\}_{k=0}^\infty$ a sequence of continuous mappings $T_{k}: X_{k} \to X_{k+1}$. The pair $(\boldsymbol{X},\boldsymbol{T})$ is…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
This paper exhibits the closed-loop design constraints using the non-analytic function theory. First, the paper generalizes the sensitivity integral for linear feedback systems with the non-analytic sensitivity function. Sensitivity…
The aim of this research is to introduce the notion of multi-transitivity in non-autonomous discrete dynamical systems(NDDS) with respect to a vector. Necessary and sufficient conditions are obtained under which a NDDS is multitransitive…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…
We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these…
Consciousness and intelligence are properties commonly understood as dependent by folk psychology and society in general. The term artificial intelligence and the kind of problems that it managed to solve in the recent years has been shown…
Despite the rapid development and great success of machine learning models, extensive studies have exposed their disadvantage of inheriting latent discrimination and societal bias from the training data. This phenomenon hinders their…
For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It…
Atoms and molecules can serve as sensitive probes of a possible variation of the fine structure constant $\alpha$ and electron-to-proton mass ratio $\mu$. Two types of sensitivity coefficients are often used to quantify and compare the…
Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient…
We generalize notions of passivity and dissipativity to fractional order systems. Similar to integer order systems, we show that the proposed definitions generate analogous stability and compositionality properties for fractional order…
Let $X$ be a Peano continuum having a free arc and let $C^0(X)$ be the semigroup of continuous self-maps of $X$. A subsemigroup $F\subset C^0(X)$ is said to be sensitive, if there is some constant $c>0$ such that for any nonempty open set…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the…