Related papers: Visualizing the logistic map with a microcontrolle…
The increased availability of interactive maps on the Internet and on personal mobile devices has created new challenges in computational cartography and, in particular, for label placement in maps. Operations like rotation, zoom, and…
We map the phase-space trajectories of an external-cavity semiconductor laser using phase portraits. This is both a visualization tool as well as a thoroughly quantitative approach enabling unprecedented insight into the dynamical regimes,…
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…
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…
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a…
This paper extends our previous work in [1],[2], on optimal scheduling of autonomous vehicle arrivals at intersections, from one to a grid of intersections. A scalable distributed Mixed Integer Linear Program (MILP) is devised that solves…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
Simplicity bias is an intriguing phenomenon prevalent in various input-output maps, characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these maps typically feature high-probability outputs with simple…
Optimal path planning and control of microscopic devices navigating in fluid environments is essential for applications ranging from targeted drug delivery to environmental monitoring. These tasks are challenging due to the complexity of…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…
We study the effect of a weak random additive noise in a linear chain of N locally-coupled logistic maps at the edge of chaos. Maps tend to synchronize for a strong enough coupling, but if a weak noise is added, very intermittent…
We investigate the effects of linear and optimal nonlinear control in the simple case of one-dimensional unimodal maps. We show that linear feedback relates unimodal maps to invertible ``Henon-like'' maps. This observation should be useful…
We experimentally report on the detection of chaos from a free-running commercial broad-area VCSEL without the need for external perturbation such as optical feedback, injection or current modulation. The evolution of nonlinear dynamics…
We show how light can be controllably transported by light at microscale dimensions. We design a miniature device which consists of a short segment of an optical fiber coupled to transversely-oriented input-output microfibers. A whispering…
The quasiperiodic route to chaos in a piecewise linear forced parallel LCR circuit with a negative conductance and diode is studied analytically. An explicit analytical solution for the normalized state equations of the piecewise linear…
Electronic circuits can be separated into two groups, digital and analog circuits. Analog circuits operate on analog quantities that are continuous in value, whereas digital circuits operate on digital quantities that are discrete in value…
Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…