Rhythmic behavior of social insects from single to multibody

Revealing the evolution of well-organized social behavior requires understanding a mechanism by which collective behavior is produced. A well-organized group may be produced by two possible mechanisms, namely, a central control and a distributed control. In the second case, local interactions between interchangeable components function at the bottom of the collective behavior. We focused on a simple behavior of an individual ant and analyzed the interactions between a pair of ants. In an experimental set-up, we placed the workers in a hemisphere without a nest, food, and a queen, and recorded their trajectories. The temporal pattern of velocity of each ant was obtained. From this bottom-up approach, we found the characteristic behavior of a single worker and a pair of workers as follows: (1) Activity of each individual has a rhythmic component. (2) Interactions between a pair of individuals result in two types of coupling, namely the anti-phase and the in-phase coupling. The direct physical contacts between the pair of workers might cause a phase shift of the rhythmic components in individual ants. We also build up a simple model based on the coupled oscillators toward the understanding of the whole colony behavior.

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.

Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation

This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods. Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules. Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments. Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV. Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).

A generic, hard transition to chaos

A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive values of a parameter F, no matter how small, a fully developed chaotic attractor exists within some domain of additional parameters, whereas no chaotic behavior exists for F < 0. As F is made positive, an unstable fixed point reaches an invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic structure existing at F = 0 make the limits t --* +oc, F ~ +0 non-commuting, and allow an exact description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators in near-resonance at any 2 : q frequency ratio, with F representing linear excitation of the first oscillator) is fully analysed

Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

Transiciones irreversibles en redes complejas

En esta tesis se aborda la emergencia de sincronización en sistemas de osciladores acoplados. En particular, nos centraremos en la emergencia de un tipo de transición discontinua entre el estado incoherente y el estado síncrono, llamada transición explosiva. Este fenómeno es análogo al de las transiciones de fase de primer orden asociadas a los cambios de agregación de la materia, cuya importancia abarca diversos campos, desde la sincronización espontánea de redes neuronales al riesgo de desincronización súbita entre los osciladores que componen la red de suministro de potencia eléctrica. Para analizar el problema, se introducen varios métodos de creciente generalidad cuyo efecto es inducir una transición explosiva al imponer una serie condiciones sobre la topología y las frecuencias naturales de cada oscilador. Así mismo, se aborda el estudio de un modelo algo más complejo con características similares para entender en mayor profundidad las características asociadas a este tipo de transiciones, siendo la histéresis una de las más destacadas. Finalmente, se propone un método cuantitativo para describir la importancia de cada nodo en el proceso de sincronización con el objetivo de estudiar y caracterizar el efecto sobre los nodos del sistema de los diversos métodos que inducen una transición explosiva. Este nuevo enfoque permite descubrir un proceso de frustración de la sincronización local en redes de osciladores acoplados, siendo el responsable de la emergencia de la sincronización explosiva. ABSTRACT In this thesis we address the emergence of synchronization in systems of coupled oscillators in complex networks. We focus our attention on a particular kind of discontinuous transitions, named explosive synchronization, where the system changes abruptly from an incoherent state to a synchronous state. This emergent phenomena is analogous to those first order transitions typically associated with changes among the aggregate states of matter, and it is important in many different fields, such as spontaneous synchronization of neurons or spontaneous desynchronization in power grids. To analyze it, we introduce some methods of increasing generality in order to induce such a discontinuous transition by acting over the topology and the natural frequencies in several different ways. Likewise, we address the study of a more complex model in order to acquire deeper knowledge on the properties of this kind of transitions, where a hysteretic behavior is specially relevant. Finally, we propose a new quantitative approach in order to find the importance of each node in the route to synchronization, aiming to provide a characterization of the effects over the network’s units of the different methods able to induce an explosive transition. This approach allows us to show the inner mechanisms behind such explosive behavior in networks of coupled oscillators, being rooted by a frustration of the local synchronization process previous to the emergence of global coherence.

Design and fabrication of a nonlinear micro impact oscillator

In this paper we describe the design and fabrication of a mechanical autonomous impact oscillator with a MEMS resonator as the frequency control element. The design has been developed with scalability to large 2-D arrays of coupled oscillators in mind. The dynamic behaviour of the impact oscillator was numerically studied and it was found that the geometry nonlinearity has an effect on the static pull-in voltage and equilibrium position. The external driving power can alter the frequency of the impact oscillator. The autonomous nature of the oscillator simplifies the complexity of the drive circuitry and is essential for large 2-D arrays.

A minimal model of partial synchrony

We wish to acknowledge A Pikovsky and M Zaks for useful discussions. This work has been financially supported by the EU project COSMOS (642563).

Numerical analysis of the modal coupling at low resonances in a Colombian Andean Bandola in C using the finite element method

The work presented in this thesis is concerned with the dynamical behavior of a CBandola's acoustical box at low resonances -- Two models consisting of two and three coupled oscillators are proposed in order to analyse the response at the first two and three resonances, respectively -- These models describe the first resonances in a bandola as a combination of the lowest modes of vibration of enclosed air, top and back plates -- Physically, the coupling between these elements is caused by the fluid-structure interaction that gives rise to coupled modes of vibration for the assembled resonance box -- In this sense, the coupling in the models is expressed in terms of the ratio of effective areas and masses of the elements which is an useful parameter to control the coupling -- Numerical models are developed for the analysis of modal coupling which is performed using the Finite Element Method -- First, it is analysed the modal behavior of separate elements: enclosed air, top plate and back plate -- This step is important to identify participating modes in the coupling -- Then, a numerical model of the resonance box is used to compute the coupled modes -- The computation of normal modes of vibration was executed in the frequency range of 0-800Hz -- Although the introduced models of coupled oscillators only predict maximum the first three resonances, they also allow to study qualitatively the coupling between the rest of the computed modes in the range -- Considering that dynamic response of a structure can be described in terms of the modal parameters, this work represents, in a good approach, the basic behavior of a CBandola, although experimental measurements are suggested as further work to verify the obtained results and get more information about some characteristics of the coupled modes, for instance, the phase of vibration of the air mode and the radiation e ciency

Existence and wandering of bumps in a spiking neural network model

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to those of the standard Amari model. For non-slow synaptic connections we are able to go beyond the standard firing rate analysis of localized solutions allowing us to explicitly construct a family of co-existing one-bump solutions, and then track bump width and firing pattern as a function of system parameters. We also present an analysis of the model on a discrete lattice. We show that multiple width bump states can co-exist and uncover a mechanism for bump wandering linked to the speed of synaptic processing. Moreover, beyond a wandering transition point we show that the bump undergoes an effective random walk with a diffusion coefficient that scales exponentially with the rate of synaptic processing and linearly with the lattice spacing.

Components and circuits for tunneling diode based high frequency sources

Terahertz (THz) technology has been generating a lot of interest because of the potential applications for systems working in this frequency range. However, to fully achieve this potential, effective and efficient ways of generating controlled signals in the terahertz range are required. Devices that exhibit negative differential resistance (NDR) in a region of their current-voltage (I-V ) characteristics have been used in circuits for the generation of radio frequency signals. Of all of these NDR devices, resonant tunneling diode (RTD) oscillators, with their ability to oscillate in the THz range are considered as one of the most promising solid-state sources for terahertz signal generation at room temperature. There are however limitations and challenges with these devices, from inherent low output power usually in the range of micro-watts (uW) for RTD oscillators when milli-watts (mW) are desired. At device level, parasitic oscillations caused by the biasing line inductance when the device is biased in the NDR region prevent accurate device characterisation, which in turn prevents device modelling for computer simulations. This thesis describes work on I-V characterisation of tunnel diode (TD) and RTD (fabricated by Dr. Jue Wang) devices, and the radio frequency (RF) characterisation and small signal modelling of RTDs. The thesis also describes the design and measurement of hybrid TD oscillators for higher output power and the design and measurement of a planar Yagi antenna (fabricated by Khalid Alharbi) for THz applications. To enable oscillation free current-voltage characterisation of tunnel diodes, a commonly employed method is the use of a suitable resistor connected across the device to make the total differential resistance in the NDR region positive. However, this approach is not without problems as the value of the resistor has to satisfy certain conditions or else bias oscillations would still be present in the NDR region of the measured I-V characteristics. This method is difficult to use for RTDs which are fabricated on wafer due to the discrepancies in designed and actual resistance values of fabricated resistors using thin film technology. In this work, using pulsed DC rather than static DC measurements during device characterisation were shown to give accurate characteristics in the NDR region without the need for a stabilisation resistor. This approach allows for direct oscillation free characterisation for devices. Experimental results show that the I-V characterisation of tunnel diodes and RTD devices free of bias oscillations in the NDR region can be made. In this work, a new power-combining topology to address the limitations of low output power of TD and RTD oscillators is presented. The design employs the use of two oscillators biased separately, but with the combined output power from both collected at a single load. Compared to previous approaches, this method keeps the frequency of oscillation of the combined oscillators the same as for one of the oscillators. Experimental results with a hybrid circuit using two tunnel diode oscillators compared with a single oscillator design with similar values shows that the coupled oscillators produce double the output RF power of the single oscillator. This topology can be scaled for higher (up to terahertz) frequencies in the future by using RTD oscillators. Finally, a broadband Yagi antenna suitable for wireless communication at terahertz frequencies is presented in this thesis. The return loss of the antenna showed that the bandwidth is larger than the measured range (140-220 GHz). A new method was used to characterise the radiation pattern of the antenna in the E-plane. This was carried out on-wafer and the measured radiation pattern showed good agreement with the simulated pattern. In summary, this work makes important contributions to the accurate characterisation and modelling of TDs and RTDs, circuit-based techniques for power combining of high frequency TD or RTD oscillators, and to antennas suitable for on chip integration with high frequency oscillators.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.