33 research outputs found
Complex order van der Pol oscillator
In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed
Fractional central pattern generators for bipedal locomotion
Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots.
In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity
Dynamical Analysis and Visualization of Tornadoes Time Series
In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective
of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus
cloud down to the ground. Such phenomena reveal features that are well described
by power law functions and unveil characteristics found in systems with long range
memory effects. Tornado time series are viewed as the output of a complex system and are
interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of
Dirac impulses with amplitude proportional to the events size. First, a collection of time series
involving 64 years is analyzed in the frequency domain by means of the Fourier transform.
The amplitude spectra are approximated by power law functions and their parameters
are read as an underlying signature of the system dynamics. Second, it is adopted the concept
of circular time and the collective behavior of tornadoes analyzed. Clustering techniques
are then adopted to identify and visualize the emerging patterns
Bipedal Locomotion: A Fractional CPG for Generating Patterns
Proceedings of the 10th Conference on Dynamical Systems Theory and ApplicationsThere has been an increase interest in the study of animal locomotion. Many models for the generation of locomotion patterns of different animals, such as centipedes, millipedes, quadrupeds, hexapods, bipeds, have been proposed.
The main goal is the understanding of the neural bases that are behind animal locomotion. In vertebrates, goal-directed locomotion is a complex task, involving the central pattern generators located somewhere in the spinal cord, the brainstem command systems for locomotion, the control systems for steering and control of body orientation, and the neural structures responsible for the selection of motor primitives.
In this paper, we focus in the neural networks that send signals to the muscle groups in each joint, the so-called central pattern generators (CPGs). We consider a fractional version of a CPG model for locomotion in bipeds. A fractional derivative) Dα f (x), with α non-integer, is a generalization of the concept of an integer derivative, where α = 1 The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a four cells model, where each cell is modelled by a system of ordinary differential equations. The coupling between the cells allows two independent permutations, and, as so, the system has D2 symmetry. We consider 0 < α ≤ 1 and we compute, for each value of α, the amplitude and the period of the periodic solutions identified with two legs' patterns in bipeds. We find the amplitude and the period increase as α varies from zero up to one
Visualizing control systems performance: A fractional perspective
This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities
New Features to Look at Natural Phenomena
Proceeding of the 3rd International Conference on Fractional Systems and Signals, at Ghent, BelgiumThe paper focuses the patterns seen in the number of victims from natural catastrophic phenomena. We consider the number of victims of storms from 1900 up to 2013 in 11 countries and study the distributions of the events with more than 30 deadly victims. The similarities among events across the 11 countries are analysed using agglomerative hierarchical clustering. Countries belonging to the same cluster are similar with respect to fatalities. Power laws and hierarchical clustering provide comparable results for the data. Future work is needed in order to explore these numerical tools in more countries and in victims of other hazards
The Persistence of Memory
This paper analyzes several natural and
man-made complex phenomena in the perspective of
dynamical systems. Such phenomena are often characterized
by the absence of a characteristic length-scale,
long range correlations and persistent memory, which
are features also associated to fractional order systems.
For each system, the output, interpreted as a manifestation
of the system dynamics, is analyzed by means
of the Fourier transform. The amplitude spectrum is
approximated by a power law function and the parameters
are interpreted as an underlying signature of the
system dynamics. The complex systems under analysis
are then compared in a global perspective in order to
unveil and visualize hidden relationships among them
A Fractional Perspective to the Bond Graph Modelling of World Economies
Inspired in dynamic systems theory and Brewer’s contributions to apply it to economics, this paper establishes a bond graph model. Two main variables, a set of inter-connectivities based on nodes and links (bonds) and a fractional order dynamical perspective, prove to be a good macro-economic representation of countries’ potential performance in nowadays globalization. The estimations based on time series for 50 countries throughout the last 50 decades confirm the accuracy of the model and the importance of scale for economic performance
A review of power laws in real life phenomena
Power law distributions, also known as heavy tail distributions, model distinct real life
phenomena in the areas of biology, demography, computer science, economics, information
theory, language, and astronomy, amongst others. In this paper, it is presented a
review of the literature having in mind applications and possible explanations for the
use of power laws in real phenomena. We also unravel some controversies around power
laws
Double power laws, fractals and self-similarity
Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data