Nonlinear channelizer.

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal.

Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion.

The rich dynamical behavior stemming from unidirectional coupling in a single array of overdamped nonlinear elements has, recently, been extensively studied. By adjusting control parameters, one obtains regimes of oscillations with a frequency that scales in a characteristic way with the control parameter. With an external time-sinusoidal driving signal, a richness of synchronized (to the drive frequency or its subharmonics depending on the control parameter) dynamical behavior ensues.

Complex behavior in driven unidirectionally coupled overdamped Duffing elements.

It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations (corresponding to transitions between the stable steady states of each nonlinear element) when a control parameter exceeds a threshold value. In recent publications [A.

Complex dynamics in unidirectionally coupled overdamped bistable systems subject to a time-periodic external signal.

Recently, we have studied the emergence of oscillatory behavior in overdamped undriven nonlinear dynamic systems subject to carefully crafted coupling schemes and operating conditions [V. In, Phys. Rev.

Multifrequency synthesis using two coupled nonlinear oscillator arrays.

We illustrate a scheme that exploits the theory of symmetry-breaking bifurcations for generating a spatio-temporal pattern in which one of two interconnected arrays, each with N Van der Pol oscillators, oscillates at N times the frequency of the other. A bifurcation analysis demonstrates that this type of frequency generation cannot be realized without the mutual interaction between the two arrays. It is also demonstrated that the mechanism for generating these frequencies between the two arrays is different from that of a master-slave interaction, a synchronization effect, or that of subharmonic and ultraharmonic solutions generated by forced systems.

Emergent oscillations in unidirectionally coupled overdamped bistable systems.

It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations when a control parameter exceeds a threshold value. In a recent publication [Phys.

Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators.

Frequency-related oscillations in coupled oscillator systems, in which one or more oscillators oscillate at different frequencies than the other oscillators, have been studied using group theoretical methods by Armbruster and Chossat [Phys. Lett. A 254, 269 (1999)] and more recently by Golubitsky and Stewart [in Geometry, Mechanics, and Dynamics, edited by P.

Coupling-induced oscillations in overdamped bistable systems.

It is well known that overdamped and unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations when a control parameter exceeds a threshold value. We demonstrate this effect in a specific system, a soft-potential mean-field description of the dynamics in a (hysteretic) single-domain ferromagnetic sample.