An alternative solution to the model structure selection problem

An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model

Probing the dynamics of identified neurons with a data-driven modeling approach

In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach

Electronically--implemented coupled logistic maps

The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics. In this work, we design and characterize a simple, low-cost, easy-to-handle, electronic implementation of the logistic map. In particular, our implementation allows for straightforward circuit-modifications to behave as different one-dimensional discrete-time systems. Also, we design a coupling block in order to address the behavior of two coupled maps, although, our design is unrestricted to the discrete-time system implementation and it can be generalized to handle coupling between many dynamical systems, as in a complex system. Our findings show that the isolated and coupled maps' behavior has a remarkable agreement between the experiments and the simulations, even when fine-tuning the parameters with a resolution of $\sim 10^{-3}$. We support these conclusions by comparing the Lyapunov exponents, periodicity of the orbits, and phase portraits of the numerical and experimental data for a wide range of coupling strengths and map's parameters.Comment: 8 pages, 10 figure

Adaptive Detection of Instabilities: An Experimental Feasibility Study

We present an example of the practical implementation of a protocol for experimental bifurcation detection based on on-line identification and feedback control ideas. The idea is to couple the experiment with an on-line computer-assisted identification/feedback protocol so that the closed-loop system will converge to the open-loop bifurcation points. We demonstrate the applicability of this instability detection method by real-time, computer-assisted detection of period doubling bifurcations of an electronic circuit; the circuit implements an analog realization of the Roessler system. The method succeeds in locating the bifurcation points even in the presence of modest experimental uncertainties, noise and limited resolution. The results presented here include bifurcation detection experiments that rely on measurements of a single state variable and delay-based phase space reconstruction, as well as an example of tracing entire segments of a codimension-1 bifurcation boundary in two parameter space.Comment: 29 pages, Latex 2.09, 10 figures in encapsulated postscript format (eps), need psfig macro to include them. Submitted to Physica

Parameter identification of BIPT system using chaotic-enhanced fruit fly optimization algorithm

Bidirectional inductive power transfer (BIPT) system facilitates contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. Typically, this system is nonlinear high order system which includes nonlinear switch components and resonant networks, developing of accurate model is a challenging task. In this paper, a novel technique for parameter identification of a BIPT system is presented by using chaotic-enhanced fruit fly optimization algorithm (CFOA). The fruit fly optimization algorithm (FOA) is a new meta-heuristic technique based on the swarm behavior of the fruit fly. This paper proposes a novel CFOA, which employs chaotic sequence to enhance the global optimization capacity of original FOA. The parameter identification of the BIPT system is formalized as a multi-dimensional optimization problem, and an objective function is established minimizing the errors between the estimated and measured values. All the 11 parameters of this system (Lpi, LT, Lsi, Lso, CT, Cs, M, Rpi, RT, Rsi and Rso) can be identified simultaneously using measured input–output data. Simulations show that the proposed parameter identification technique is robust to measurements noise and variation of operation condition and thus it is suitable for practical application

Integrated chaos generators

This paper surveys the different design issues, from mathematical model to silicon, involved on the design of integrated circuits for the generation of chaotic behavior.Comisión Interministerial de Ciencia y Tecnología 1FD97-1611(TIC)European Commission ESPRIT 3110

Bifurcations and synchronization using an integrated programmable chaotic circuit

This paper presents a CMOS chip which can act as an autonomous stand-alone unit to generate different real-time chaotic behaviors by changing a few external bias currents. In particular, by changing one of these bias currents, the chip provides different examples of a period-doubling route to chaos. We present experimental orbits and attractors, time waveforms and power spectra measured from the chip. By using two chip units, experiments on synchronization can be carried out as well in real-time. Measurements are presented for the following synchronization schemes: linear coupling, drive-response and inverse system. Experimental statistical characterizations associated to these schemes are also presented. We also outline the possible use of the chip for chaotic encryption of audio signals. Finally, for completeness, the paper includes also a brief description of the chip design procedure and its internal circuitry

A mixed-signal integrated circuit for FM-DCSK modulation

This paper presents a mixed-signal application-specific integrated circuit (ASIC) for a frequency-modulated differential chaos shift keying (FM-DCSK) communication system. The chip is conceived to serve as an experimental platform for the evaluation of the FM-DCSK modulation scheme, and includes several programming features toward this goal. The operation of the ASIC is herein illustrated for a data rate of 500 kb/s and a transmission bandwidth in the range of 17 MHz. Using signals acquired from the test platform, bit error rate (BER) estimations of the overall FM-DCSK communication link have been obtained assuming wireless transmission at the 2.4-GHz ISM band. Under all tested propagation conditions, including multipath effects, the system obtains a BER = 10-3 for Eb/No lower than 28 dB.Ministerio de Ciencia y Tecnología TIC2003-0235

CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit

This paper presents design considerations for monolithic implementation of piecewise-linear (PWL) dynamic systems in CMOS technology. Starting from a review of available CMOS circuit primitives and their respective merits and drawbacks, the paper proposes a synthesis approach for PWL dynamic systems, based on state-variable methods, and identifies the associated analog operators. The GmC approach, combining quasi-linear VCCS's, PWL VCCS's, and capacitors is then explored regarding the implementation of these operators. CMOS basic building blocks for the realization of the quasi-linear VCCS's and PWL VCCS's are presented and applied to design a Chua's circuit IC. The influence of GmC parasitics on the performance of dynamic PWL systems is illustrated through this example. Measured chaotic attractors from a Chua's circuit prototype are given. The prototype has been fabricated in a 2.4- mu m double-poly n-well CMOS technology, and occupies 0.35 mm/sup 2/, with a power consumption of 1.6 mW for a +or-2.5-V symmetric supply. Measurements show bifurcation toward a double-scroll Chua's attractor by changing a bias current