Related Experiment Videos
Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation
Yassine Boubendir1, Vicenç Méndez, Horacio G Rotstein
1Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102, USA.
Abstract:
We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.
Related Concept Videos
Time-Domain Interpretation of PD Control
Consider the example of control of motor torque. Initially, a positive...
Feedback control systems
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Second Order systems II
If ζ...
Control System Problem
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
Effects of feedback
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
Relation between Mathematical Equations and Block Diagrams