Related papers: Analysis of Periodic Feedback Shift Registers
We determine the cycle structure of linear feedback shift register with arbitrary monic characteristic polynomial over any finite field. For each cycle, a method to find a state and a new way to represent the state are proposed.
Feedback shift registers(FSRs) are a fundamental component in electronics and secure communication. An FSR $f$ is said to be reducible if all the output sequences of another FSR $g$ can also be generated by $f$ and the FSR $g$ has less…
In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \[ x^{\Delta}(t)=A(t)x(t)+Q^{\Delta}\left(t,x\left(\delta_{-}(s,t)\right) \right)…
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on…
Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution…
The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated…
Floquet dynamical quantum phase transitions (FDQPTs) reveal many nonequilibrium critical phenomena in periodically driven quantum systems, and their underlying mechanisms have attracted deep attention in recent years. In this paper, we…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
When the Poincar\'{e} map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby…
Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the…
Periodically driven quantum systems can function as highly selective parameter filters. We demonstrate this capability in a finite-size, three-qubit system described by the transverse-field Floquet Ising model. In this system, we identify a…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
Long-period systems and superlattices, with additional periodicity, have new effects on the energy spectrum and wave functions. Most approaches adjust theories for infinite systems, which is acceptable for large but not small number of unit…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
This paper develops and implements an algorithm to compute sequences of polytopic Robust Forward Invariant Sets (RFIS) that can parametrically vary in size between the maximal and minimal RFIS of a nonlinear dynamical system. This is done…
This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger…
Much recent experimental effort has focused on the realization of exotic quantum states and dynamics predicted to occur in periodically driven systems. But how robust are the sought-after features, such as Floquet topological surface…
This paper presents an active inference method for Extended Finite State Machines, where inputs and outputs are parametrized, and transitions can be conditioned by guards involving input parameters and internal variables called registers.…
We present a comprehensive theoretical framework for calculating the linear and nonlinear optical responses of time-periodic quantum systems. Using density matrix evolution in the Floquet basis and adopting the length gauge, our approach…