Narrow Results

The dynamic behavior of first-order autonomous space invariant cellular neural networks (CNNs) is investigated. It is shown that complex dynamics may occur in very simple CNN structures, described by two-dimensional templates that present only vertical and horizontal couplings. The bifurcation processes are analyzed through the computation of the limit cycle Floquet's multipliers, the evaluation of the Lyapunov exponents and of the signal spectra. As a main result a detailed and accurate two-dimensional bifurcation diagram is reported. The diagram allows one to distinguish several regions in the parameter space of a single CNN. They correspond to stable, periodic, quasi-periodic, and chaotic behavior, respectively. In particular it is shown that chaotic regions can be reached through two different routes: period doubling and torus breakdown. We remark that most practical CNN implementations exploit first order cells and space-invariant templates: so far only a few examples of complex dynamics and no complete bifurcation analysis have been presented for such networks.

A generic model for second-order RC sinusoidal oscillators is derived. The model is based on treating an oscillator as a second-order passive network, with an arbitrary unknown structure, terminated at one port by a linear voltage-controlled negative resistor. A modified model which takes into account the fundamentally nonlinear characteristics of the negative resistor is also derived.

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown.

We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described.

We show a mixer circuit that exhibits infinitely high third-order intercept point (IP3) over a range of RF input levels. It follows from this fact that IP3 is not adequate for characterizing mixers. The formula for calculating IP3 from fundamental- and third-order intermodulation products at a single RF input level is not valid for the mentioned mixer over an RF input power range. Instead of IP3, we suggest a replacement.

This paper presents six different meminductor emulator circuits based on operational amplifiers. Five circuits of meminductor emulators have been proposed using two operational amplifiers, one memristor, three resistors and one capacitor, whereas the sixth circuit uses two operational amplifiers, two memristors, one resistor and two capacitors. All circuits of the proposed meminductor emulators are very simple over most of the realizations of meminductor emulators in the literature. The behaviors of meminductor emulators are satisfactory over a wide range of frequencies. The proposed configurations of meminductor emulators have been simulated by the LTspice tool. The SPICE models of both operational amplifier (AD711) and memristor have been used for simulation. The workability of the proposed meminductor emulators has also been verified using the basic and well-known structure of operational amplifier. In addition, the pinched hysteresis loop obtained by the simulation results of meminductor emulator has been achieved by the experimental results as well. Chaotic oscillator has been designed using the proposed meminductor emulator to prove the worthiness of the design.

Cellular neural networks have found applications both as a platform for high speed image processing, as well as a model for complex spatiotemporal dynamical phenomena. This paper describes spatial pattern formation in a CMOS VLSI implementation of a CNN. With four layers of 32×64 cells, this CNN contains the most recurrently interconnected 2D layers of any VLSI CNN implementation to date. With over 8000 cells, it is also one of the largest in terms of the total number of cells. The spatial patterns generated by this network are bands of activity with a preferred scale and orientation, both of which can be adjusted via external bias voltages. The VLSI implementation provides a physical substrate for experimenting with complex spatiotemporal phenomena in real time, while also being amenable to theoretical analysis. Our experimental characterization of the observed patterns are in excellent agreement with our theoretical predictions.

How fluctuations can be eliminated or attenuated is a matter of general interest in the study of steadily-forced dissipative nonlinear dynamical systems. Here, we extend previous work on "nonlinear quenching" [Hide, 1997] by investigating the phenomenon in systems governed by the novel autonomous set of nonlinear ordinary differential equations (ODE's) , ẏ=-xzq+bx-y and ż=xyq-cz (where (x, y, z) are time(t)-dependent dimensionless variables and , etc.) in representative cases when q, the "quenching function", satisfies q=1-e+ey with 0≤e≤1. Control parameter space based on a,b and c can be divided into two "regions", an S-region where the persistent solutions that remain after initial transients have died away are steady, and an F-region where persistent solutions fluctuate indefinitely. The "Hopf boundary" between the two regions is located where b=b_H(a, c; e) (say), with the much studied point (a, b, c)=(10, 28, 8/3), where the persistent "Lorenzian" chaos that arises in the case when e=0 was first found lying close to b=b_H(a, c; 0). As e increases from zero the S-region expands in total "volume" at the expense of F-region, which disappears altogether when e=1 leaving persistent solutions that are steady throughout the entire parameter space.

The dynamics of propagating interfaces in a bistable neural network is investigated. We consider the network composed of two coupled 1D lattices and assume that they interact in a local spatial point (pin contact). The network unit is modeled by the FitzHugh–Nagumo-like system in a bistable oscillator mode. The interfaces describe the transition of the network units from the rest (unexcited) state to the excited state where each unit exhibits periodic sequences of excitation pulses or action potentials. We show how the localized inter-layer interaction provides an "excitatory" or "inhibitory" action to the oscillatory activity. In particular, we describe the interface propagation failure and the initiation of spreading activity due to the pin contact. We provide analytical results, computer simulations and physical experiments with two-layer electronic arrays of bistable cells.

We investigate Coherence Resonance phenomenon in an electronic circuit obeying the FitzHugh–Nagumo dynamics. The phenomenon is induced with a noise source exhibiting different nature. The resonance behavior results are significantly reinforced when experimental parameters are tuned in order to place the stable fixed point closer to the excitability threshold of spiking behavior, as well as when the time scales of the circuit are properly modified.

We have recently proposed a Cellular Nonlinear Network (CNN) based on nonlinear oscillator properties to perform image processing tasks. We present here the electronic implementation of the elementary cell of this CNN. We experimentally verify the main property of the CNN, that is the possibility to enhance a weak difference of initial condition between two specific cells of the CNN at a given time. For this optimal time, a contrast enhancement of a weak contrasted gray scale is possible.

In this paper, we discuss an efficient iterative method for the estimation of the chief dynamical invariants of chaotic systems based on stochastically stable piecewise affine maps (e.g. the invariant measure, the Lyapunov exponent as well as the Kolmogorov–Sinai entropy). The proposed method represents an alternative to the Monte-Carlo methods and to other methods based on the discretization of the Frobenius–Perron operator, such as the well known Ulam's method. The proposed estimation method converges not slower than exponentially and it requires a computation complexity that grows linearly with the iterations. Referring to the theory developed by C. Liverani, we discuss a theoretical tool for calculating a conservative estimation of the convergence rate of the proposed method. The proposed approach can be used to efficiently estimate any order statistics of a symbolic source based on a piecewise affine mixing map.

The experimental study of in-out intermittency during the incomplete synchronization of two coupled, nonlinear, autonomous, fourth-order, chaotic, circuits is reported. The two circuits are unidirectionally coupled via a linear resistor. The dependence of laminar lengths, on the deviation of the control parameter from its critical value, and the mean laminar length distribution, are studied.

In this paper, a new chaotic circuit is introduced, conceived by considering a Colpitts oscillator with the inclusion of two further elements: a coupled inductor and a variable resistor. The proposed circuit exhibits a rich dynamics that has been experimentally characterized through the bifurcation diagram with respect to the resistor value. The main result that can be derived from the analysis of the new circuit leads to a simple way to control chaos in the chaotic Colpitts oscillator by varying a single external control parameter. The same technique has then been applied to the classical periodic Colpitts oscillator, demonstrating how in this way the oscillation frequency can be controlled.

Memristors are gaining increasing interest in the scientific community for their possible applications, e.g. high-speed low-power processors or new biological models for associative memories. Due to the intrinsic nonlinear characteristic of memristive devices, it is possible to use them in the design of new dynamical circuits that are able to show complex behavior, like chaos. In this paper, two new memristive chaotic circuits are presented discussing, in particular, an approach based on Cellular Nonlinear Networks for the implementation of the memristive device. The approach investigated in this paper allows to obtain memristors with common off-the-shelf components and to observe the onset of new chaotic attractors in nonlinear circuits with memristors. Furthermore, the circuits presented in this paper, being the first examples of memristive chaotic circuits based on CNNs, can be considered as the link between the three inventions by Leon O. Chua, i.e. the memristor, the first chaotic electronic circuit and Cellular Nonlinear Networks.

In this paper, experimental results showing that the dynamics of Chua's circuit can be controlled by using water electrolytic cell based devices are reported. A Chua's circuit where one of the electrical components is replaced by an electrolytic cell device has been realized and its dynamics has been studied showing how different regimes appear when the parameters of the cell (in particular, the level of immersion of the electrode plates and the distance between them) are changed. The results obtained pave the way to the possibility of coupling nonlinear electronic components with electrochemical devices so as to develop a new hybrid technology for implementing a new class of nonlinear circuits.

In this paper, the dynamics of Chua's circuit in jerk form is presented. It is proved that two forms of Chua's circuit in jerk dynamics can be derived. The electronic circuit of the simpler dynamics has been implemented. The link between Chua's circuit and the search for simple jerk circuits has been established, therefore, proposing complex dynamics (like that of Chua's circuit) in jerk form.

The occurrence of an hysteretic loop in the frequency response of a driven nonlinear system is a phenomenon deeply investigated in nonlinear control theory. Such a phenomenon, which is linked to the multistable behavior of the system, is called jump resonance, since the magnitude of the frequency response is subjected to an abrupt jump up/down with respect to the increasing/decreasing of the frequency of the driving signal. In this paper, we aim at investigating fractional order nonlinear systems showing jump resonance, that is systems in which the order of the derivative is noninteger and their frequency response has a magnitude that is a multivalued function in a given range of frequencies. Furthermore, a strategy for designing fractional order systems showing jump resonance is presented along with the procedure to design and implement an analog circuit based on the approximation of the fractional order derivative. An extensive numerical analysis allows one to assess that the phenomenon is robust to the difference in the derivative order, enlightening the first example of a system with order lower than two which is able to demonstrate a jump resonance behavior.

In this paper, we focus on the thermal characterization of nonlinear electronic circuits deriving some conditions which suggest the existence of a relationship with the specific dynamic behavior shown by the circuit. A series of thermographic experiments indicate that the chaotic behavior in electronic circuits is associated with slower thermal transients, a slow linear growth of the temperature during the normal operating regime and lower overall temperature increase with respect to other dynamical regimes. Three experimental case studies are reported and discussed, considering also the effect of chaos control strategies.

The design of a screw-type chaotic system in is presented whereby the dynamical equations are constructed using geometric methods that produce a vector field with the desired properties. We utilize piecewise linear and constant dynamics for simplicity; the piecemeal dynamics are combined using switching functions. An analysis of the system shows invariance and the absence of equilibria — implying the existence of limit cycles and strange attractors; a bifurcation diagram confirms the existence of these behavioral modes and that the system undergoes a period-doubling cascade to chaos. We finally present a hardware realization of this system, and oscilloscope traces showing a chaotic system trajectory.