Delayed-feedback control of spatial bifurcations and chaos in open-flow models

Amplitude death phenomena in delay-coupled Hamiltonian systems

Hamiltonian systems, when coupled via time-delayed interactions, do not remain conservative. In the uncoupled system, the motion can typically be periodic, quasiperiodic, or chaotic. This changes drastically when delay coupling is introduced since now attractors can be created in the phase space. In particular, for sufficiently strong coupling there can be amplitude death (AD), namely, the stabilization of point attractors and the cessation of oscillatory motion. The approach to the state of AD or oscillation death is also accompanied by a phase flip in the transient dynamics. A discussion and analysis of the phenomenology is made through an application to the specific cases of harmonic as well as anharmonic coupled oscillators, in particular the Hénon-Heiles system.

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh-Nagumo model

Elimination and control of nonlinear phenomena in excitable media are important for academic interests and practical applications. This paper provides a systematic procedure to design external forces for eliminating a traveling wave in a one-dimensional piecewise linear FitzHugh-Nagumo model. This procedure allows us to design nonfeedback and feedback control systems. The feedback control systems are designed using classical control theory. Furthermore, this procedure is extended to a two-dimensional model and verified using numerical simulation.

Modeling velocity in gradient flows with coupled-map lattices with advection

We introduce a simple model to investigate large scale behavior of gradient flows based on a lattice of coupled maps which, in addition to the usual diffusive term, incorporates advection, as an asymmetry in the coupling between nearest neighbors. This diffusive-advective model predicts traveling patterns to have velocities obeying the same scaling as wind velocities in the atmosphere, regarding the advective parameter as a sort of geostrophic wind. In addition, the velocity and wavelength of traveling wave solutions are studied. In general, due to the presence of advection, two regimes are identified: for strong diffusion the velocity varies linearly with advection, while for weak diffusion a power law is found with a characteristic exponent proportional to the diffusion.

Spatiotemporal stability and control of one-way open coupled Lorenz systems

We investigate the spatiotemporal stability of a homogeneous solution in one-way open coupled Lorenz systems, and suppress the spatial instability in the systems by using the H(infinity) control technique. The suppression is illustrated with numerical simulations. In addition, it is shown that the suppression can be also achieved for one-way ring-type systems.