University of Maryland / Duke University MURI-2007

Exploiting Nonlinear Dynamics for Novel Sensor Networks

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The unifying theme of our technical approach is that nonlinear devices and networks can be designed to be very sensitive to their environment, and that this sensitivity can be exploited to create novel sensors. By coupling the environment to the sensor system, changes in the environment will give rise to changes in the dynamics of the devices. These changes, through their networked nonlinear interactions, have the potential of effectively doing computations that discriminate patterns.

Our MURI is organized into five tasks that will demonstrate how the unifying theme can be embodied in devices that operate in different spectral regions. Tasks 1 to 4 each develop a particular device/system detector concept that, by the end of the MURI, will result in a tested prototype realization for each task. Task 5 supports the other four tasks through modeling and the development of relevant, applicable basic science.

Task 1. Radio-frequency Nonlinear Network [Task leader: Dan.Gauthier] In this task, we will develop a network of electronic chaotic nonlinear elements that offer great flexibility and simplicity. An individual element is illustrated in the figure. The central frequency of an element can be adjusted throughout a 500 MHz -10 GHz range, the bandwidth about the central frequency can be varied, and the “complexity” of the chaos can be adjusted from low to high values [Illing and Gauthier 2006]. We propose to construct multiple chaotic oscillators and investigate their behavior when they are coupled in a variety of network topologies. The coupling will be realized by an antenna that is added to the circuit to broadcast and receive signals from the other chaotic circuits in the network. Under conditions of weak coupling between oscillators, the dynamical state of each oscillator in the network will be sensitive to changes in coupling between network elements. Thus, the network will be sensitive to intrusion, which, for example, will have the effect of changing the coupling strength between elements in the network. In the strong coupling regime and for a regularly coupled network, phase or complete synchronization between elements is expected, where the phase lag/lead between elements can be varied. Such a system can be used for synthetic aperture and phased array applications (e.g., in RADAR for through-wall sensing).

Task 2. Millimeter Wave Chaotic Sensors [Task leader: John Rodgers] Sensing applications requiring high-resolution detection or precise, phased illumination of areas of interest require short wavelengths. Two bands of frequencies centered around 34 and 94 GHz have good propagation characteristics in the atmosphere and therefore will be considered. Recent studies on time-delayed traveling-wave (TDTW) oscillators have demonstrated the feasibility of generating microwave waveforms with chaotic amplitude and phase. Under certain conditions, the chaotic oscillation frequency displays repeated chirps across an extremely wide bandwidth. The accompanying figure shows the time-frequency spectrum of a chaotic TDTW oscillator operating at a center frequency of about 14 GHz [Rodgers et al. 2006], where the color indicates relative amplitude of the oscillations.


We propose a new sensing application using TDTW devices where the feedback consists partly of a fixed internal feedback to prime chaotic oscillations in the circuit and also the return signals from the external environment. The high gains in these tubes, in conjunction with the electrically long external RF path, lead to high sensitivity and widely disparate time scales, respectively, in the system dynamics. Similar to the Task 1 system, the entire region of illumination essentially becomes part of the feedback circuit and thus is encoded in the system dynamics. We will develop a TDTW oscillator system based initially on a compact millimeter-wave power module, which is a hybrid of solid state and vacuum device technologies. The chaotic dynamics of the system will be studied in relation to objects that are, for example, hidden in a large field of clutter or concealed around corners or behind barriers. In conjunction with the other proposal tasks, we will investigate signal processing circuitry and algorithms designed to extract information encoded in the chaotic dynamics, and we will also characterize the system performance in terms of probability of detection, electromagnetic and noise immunity, etc.

Task 3. Photonic Nonlinear Network [Task leader: R. Roy] In the near-infrared optical regime, networks of edge-emitting semiconductor lasers, vertical cavity surface emitting lasers (VCSELs), or diode laser pumped solid state lasers are highly efficient, low power sources of radiation that can be used to illuminate an area for surveillance. In addition, due to their relatively “open” cavities, high gain and small size, they can be used to detect changes in reflected radiation with extreme sensitivity and good spatial resolution. Recent experiments have examined instabilities in optoelectronically delay-coupled semiconductor lasers [Kim et al, 2005], and arrays of optically coupled solid state lasers. VCSEL arrays (a Fuji commercial device is shown in the above figure) are typically pumped by a source of injection current, and if the light fed back through reflection is photodetected and used to modulate the injection current of the array globally, or of individual elements or groups of elements, one may generate oscillations and waveforms that contain signatures of the nature and duration of the disturbance. We propose the use of networks of coupled lasers (e.g., VCSELs) and photodetectors to provide pattern processing and control signals, as well as significant amplification (in the range of 3 to 20 dB) for incoming signals. The signal dynamics in individual elements occurs on sub-nanosecond time scales. The ability to reconfigure modular inter-connections optically and/or electronically will provide unique speed and flexibility. These features will be realized through the use of versatile programmable liquid crystal spatial light modulators and electronic field programmable gate arrays (FPGAs). The parallel nature of these optical and electronic devices (that have now become commercially available) make them most suitable for achieving our goals. A major component of our approach will be the use of synchronization of dynamical spatio-temporal patterns for edge and motion detection, and for the identification of specific signals.

Task 4. Low Power Detection Using Wave Chaos [Task leader: Steven Anlage] Recent work by team members [e.g., Hammady et al. (2005)] and by others working in the field of ‘wave chaos' (also called ‘quantum chaos') shows that when waves of short wavelength compared to system size scatter within a complex enclosure (e.g., a room, stairwell, etc.), the results are extremely sensitive to small changes whose statistics can be extracted from the theory of random matrices. We propose to develop low-power detectors and detector networks with increased sensitivity and signal masking capability by exploiting a property of wave chaos known as fidelity. Imagine that a modulated pulse of wave energy is emitted from our device into an enclosed region. The energy fills the region and is partially reflected back to the injection port. The reflected signal (known as a coda) that is seen at the port will be widely dispersed in time (hence of low power) compared with the initial pulse. If the reflected signal is recorded, reversed in time, and sent back into the region it will reassemble in the same form as the incident pulse on reflection. This reassembly process (fidelity) occurs because the rays of the second injected signal retrace those of the original in the reversed direction. If there is a change within the region under consideration, then the second reflected signal will not reassemble into a replica of the original pulse. If the ray trajectories are chaotic, then the pulse reassembly process depends very sensitively on changes in the region under surveillance. We note that at any point in the region under surveillance, the signal would appear to be in the form of a coda rather than a sharp pulse. The pulse will only appear at the location of the detector. Because the signal (coda) is wide-band and low power, it is difficult to detect and jam. Although the above discussion has been in the context of a single detector, our scheme can be adapted to a network of sensors placed at different locations, and, in conjunction with the other tasks of our MURI, we are pursuing network aspects of this concept. Our initial effort will be to design a compact, low-power-consumption system based on ultrasound or microwaves, and to test it in various environments.

Task 5. Supporting Modeling and Basic Science [Task leader: Edward Ott] The device/network systems described above will require us to develop and apply new basic science in nonlinear dynamics. We will also pursue neuromorphically and biologically inspired concepts in designing our systems and devices; e.g., we will develop ideas aimed at configuring the networks that we will use in such a way that, through their nonlinear interactions, these networks effectively do computations that discriminate patterns. In addition, we will study and apply such basic science areas as synchronization of chaotic elements connected by networks [e.g., Restrepo et al. 2006], the effect of time delay coupling in network links, the effect of time evolution of networks as a result of movement of the network elements (e.g., for elements on UAV's [Justh and Krishnaprasad 2005]), spatio-temporal dynamics of locally and distantly coupled elements, wave chaos, numerical techniques for device and system modeling, etc. We plan to pursue these goals through a combination of theoretical, numerical and experimental approaches, and we believe that members of our team are uniquely qualified to do this. We emphasize that these basic issues are part of a unified nonlinear dynamics framework that will promote synergistic interaction and unifying research concerns throughout our team effort.


The systems we will develop will provide DoD with new, efficient sensing modalities, useful in a range of combat environments. They will work in important regions of the electromagnetic and acoustic spectra: the UHF and microwave region that is useful for through-wall sensing in urban settings, the submillimeter range that allows penetration through foliage, the infrared region that is useful for night vision applications, and the ultrasonic region that is useful for intrusion detection. The devices will also employ complex broadband signals, thus greatly degrading an enemy's ability to detect or jam operation of our sensors. Furthermore, by virtue of their simplicity, compactness and low power, our sensors will be ideally suited to providing reliable, portable operation in rugged environments, e.g., for ground troops or onboard UAV's.


The team consists of the PI (E. Ott), 9 Co-PI's at the University of Maryland , one subcontract PI at Duke University (D. Gauthier), at least one post-doc, and about 11 graduate students. The team will interact strongly, with many of the PI's participating in multiple aspects of the overall grant . Interactions are further promoted by frequent meetings of the entire team. The team is already experienced in such a multi-disciplinary approach, and many of us have had productive collaborations with each other extending beyond a decade.


S. Hammedy, X. Zheng, T. Antonsen, E. Ott, and S. Anlage. “Universal statistics of the scattering coefficient in wave chaotic systems,” Phys. Rev. E 71, 056215 (2005).

L. Illing and D. Gauthier, “Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback,” submitted to Chaos (2006).

M-Y. Kim, R. Roy, J. Aron, T. Carr, and I. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94, 88101 (2005).

E. W. Justh and P. S. Krishnaprasad, “Equilibria and steering laws for planar formations,” Control Lett. 51, 25 (2004).

J. G. Restrepo, B. R. Hunt, and E. Ott, “The emergence of coherence in complex networks of heterogeneous dynamical systems,” Phys. Rev. Lett. 96 , 254103 (2006).

J. Rodgers, T. M. Firestone, V. L. Granatstein, V. Dronov, T. M. Antonsen, Jr., and E. Ott, “Study and applications of wideband oscillations in high-power pulsed traveling-wave tubes,” Proc. IEEE Int. Conf. Plasma Science , Monterey, CA, June 2005.