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We embed 1-layer QAOA circuits into the larger class of parameterized Instantaneous Quantum Polynomial circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The use of analytic…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
We consider the problem of extraction and validation of matching rules, directly from the phased diffraction data of a quasicrystal, and propose an algorithmic procedure to produce the rules of the shortest possible range. We have developed…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
The mechanical response of amorphous solids to external strains is riddled with plastic events that create topological charges in the resulting displacement field. It was recently shown that the latter leads to screening phenomena that are…
This paper deals with various routes to hyperchaos with all three positive Lyapunov exponents in a three-dimensional quadratic map. The map under consideration displays strong hyperchaoticity in the sense that in a wider range of parameter…
In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one…
We report on the decay of a passive scalar in chaotic mixing protocols where the wall of the vessel is rotated, or a net drift of fluid elements near the wall is induced at each period. As a result the fluid domain is divided into a central…
Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and…
Recent research indicates that low-inertia viscoelastic channel flow experiences supercritical non-normal mode elastic instability from laminar to sustained chaotic flow due to finite-size perturbations. The challenge of this study is to…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
This paper studies the distribution of characteristic multipliers, the structure of submanifolds, the phase diagram, bifurcations and chaotic motions in the potential field of rotating highly irregular-shaped celestial bodies (hereafter…
We revisit the classical Suarez-Schopf delayed oscillator. Special attention is paid to the region of linear stability in the space of parameters. By means of the theory of inertial manifolds developed in our adjacent papers, we provide…
The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
In connection with the investigations of initial stages of appearance of turbulence in the current-carrying mediums and also the investigations of relaxation oscillations in thin-film bridges of high-temperature superconductor $Y Ba_2 Cu_3…
We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A…