Seth D. Cohen, Entered 2007/08
Office Location: 183 Physics
Office Phone: 919-660-2512
Email Address: firstname.lastname@example.org
Nonlinear dynamics and complex systems
BS, University of Rochester, 2007
Research Categories: Complex and Nonlinear Circuits, Ultra Wideband RF Transmission, Wave-Chaos, Sub-wavelength Imaging Techniques
Research Description: While at Duke, I have studied time-delayed feedback in oscillators in order to realize inexpensive and robust sensor systems. Conventional oscillators using time-delayed feedback use a nonlinear element whose output is amplified and coupled back to the input through a single feedback loop that delays the signal by a fixed amount. These systems can display a variety of behaviors including periodic oscillations, quasi-periodicity, and chaos. Oscillators using time-delayed feedback have been designed using high-speed commercial electronics or lasers to generate complex signals with frequency bandwidths that stretch across several gigahertz. My current research goals are to understand and exploit the broadband nature of such devices to realize sub-wavelength and other radio-frequency sensing techniques. In line with these goals, I am currently working on several experiments that utilize the complexity of the dynamics from nonlinear time-delayed feedback oscillators.
Radio-Frequency Transmission of Chaos:
The transfer of information between identical chaotic elements is of great interest in understanding the dynamics of large coupled networks. To explore the characterizations of such a network, I examined methods for radio frequency signal transmission between high-speed nonlinear oscillators. Coupling through radio transmission, rather than hard-wire connections, will allow for through-wall transmission as well as additional elements to be more easily added into the network.
Due to the broadband nature of the chaotic signal, the frequency spectrum of the high-speed chaos can fall under the category of FCC regulation 47CFR15.503 for Ultra Wideband (UWB) signals. I have also researched antennas and modulation methods that will enable bi-directional coupling between identical elements, as well as keep our transmission within legal limits. This transfer of information will be used to couple two or more of these elements in an area for further study. With small affordable devices operating within FCC regulations, the dynamics of a many bodied chaotic network can be studied in real time to evaluate current theories and explore applications in commercial technologies.
Sub-wavelength Position Sensing:
Broadband chaos has been observed previously in a simple transistor-based
nonlinear circuit with time-delayed feedback through a single coaxial cable. We have replaced this
coaxial cable with a multipath delay system consisting of broadband antennas placed inside a
stadium-shaped cavity. This creates a new nonlinear-feedback system where the multipath
reflections of the radio waves inside the cavity become the delayed-feedback loops of the
By moving a sub-wavelength scatterer that is also placed in the cavity, the
path lengths and coupling strengths of these feedback delays change. From small scatterer
movements, we observe bifurcations in the system’s output voltage between periodic, quasiperiodic,
and chaotic attractors. In between bifurcations, the dynamics respond with small shifts in peak frequency values. This enables the sub-wavelength object to be tracked to within λ/10,000. By exploiting this novel technique for
sub-wavelength sensitivity, we hope to improve traditional methods of intrusion detection
systems and tracking devices with through-wall capabilities. Furthermore, in scaling this system down to the optical domain, we predict potential applications in biological microscopy.
Sub-wavelength Position Sensing Using Optical Wavelengths
We hypothesize that resolution of our method for position sensing using nonlinear feedback and wave chaos will
scale with the wavelength of the electromagnetic radiation (EM) in the system. Therefore, in my final year, I am developing an
experimental system that reproduces our previous results.
Generalization of Quasi-periodic Frequency Shifts in Nonlinear Feedback Systems:
I am currently investigating analytically the mechanism behind our approach for subwavelength position sensing by examining bifurcations in general time-delay systems with quasiperiodic dynamics.
Low Cost Chaos-based Radar:
In recent articles, Corron et al. propose a novel chaos radar concept that uses the dynamics produced by a piecewise-linear
harmonic oscillator. This piecewise-linear system outputs a chaotic signal and a binary switching state. In a proposed radar
concept, the chaotic signal is transmitted while a copy of a switching state is stored using a one-bit sampling. In this system,
the switching state completely characterizes the dynamics of the system. For a radar receiver, Corron et al. derived a
mathematical form of a filter that is matched to the chaos produced by the system where a matched filter maximizes the
signal-to-noise ratio of a signal. The matched filter recovers the switching states from the received signal that is then passed
to a correlation operation. Correlation peaks between the recovered and stored waveforms determine the locations a targets
in the field. With reduced data storage and signal processing, this architecture could effectively reduce the overall cost of a
Corron et al. implemented their piecewise-linear design using an LRC (inductance-resistance-capacitance)
oscillator that operates in the kHz frequency ranges. It is difficult to a realize high-frequency version (> 1 GHz) of this
system because of parasitic capacitances, inductances, and the inherent time delays in the propagation of signals in LRC
circuits. As it stands, there is no high-frequency realization of the piecewise-linear system from Corron et. al or the
associated matched filter. In order to have resolutions that are comparable to state-of-the art radar systems, the waveforms
and switching states produced by this chaotic system must be scaled to higher-frequencies. I am interested in novel techniques for increasing the speed of this system.
- Seth D. Cohen, Hugo L. D. de S. Cavalcante, and Daniel J. Gauthier, Subwavelength Position Sensing Using Nonlinear Feedback,
Physical Review Letters, vol. 107 no. 25
(2011) [PhysRevLett.107.254103], [doi] [abs].
- S.D. Cohen, D. J. Gauthier, A pseudo-matched filter for chaos,
Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 22 no. 033148
(2012) [p033148_s1], [doi] [abs].
- S.D. Cohen, D. Rontani, D. J. Gauthier, Ultra-high-frequency piecewise-linear chaos using delayed feedback loops,
Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 22 no. 043112
(2012) [p043112_s1], [doi] [abs].
- G. M. Hall, E. J. Holder, S. D. Cohen, D. J. Gauthier, Low-cost chaotic radar design,
Proc. SPIE 8361, Radar Sensor Technology XVI, 836112
(2012) [proceeding.aspx], [doi] [abs].