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Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with constant impulses, the chaos can be suppressed. It is proved…
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a…
The advection of passive tracers in an oscillating vortex chain is investigated. It is shown that by adding a suitable perturbation to the ideal flow, the induced chaotic advection exhibits two remarkable properties compared with a generic…
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…
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…
We use semiclassical Hamiltonian optics to investigate the propagation of light rays through two-dimensional photonic crystals when slow spatial modulation of the lattice parameters induces mixed stable-chaotic ray dynamics. This modulation…
A procedure to enhance the quantum--classical correspondence even in situations far from the classical limit is proposed. It is based on controlling the quantum transport between classical regions using the capability to synthesize…
Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…
Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of…
A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes.…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Perturbative partial-wave amplitudes diverge in cases with a massless exchanged particle in the $t$-channel. We argue that the divergence is an artifact of perturbation theory and give a prescription for the all-orders correction factor…
Some new properties of the chaotic signal have been implemented in communication system applications recently. However, due to the broadband property of the chaotic signal, it is very difficult for a practical transducer or antenna to…
Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
Transient chaos is a characteristic behavior in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an external attractor. In some situations the escapes are highly…
Controlling Chaos could be a big factor in getting great stable amounts of energy out of small amounts of not necessarily stable resources. By definition, Chaos is getting huge changes in the system's output due to unpredictable small…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…