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

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

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals

Extracellular cysteine in connexins: Role as redox sensors

Indexación: Scopus.Connexin-based channels comprise hemichannels and gap junction channels. The opening of hemichannels allow for the flux of ions and molecules from the extracellular space into the cell and vice versa. Similarly, the opening of gap junction channels permits the diffusional exchange of ions and molecules between the cytoplasm and contacting cells. The controlled opening of hemichannels has been associated with several physiological cellular processes; thereby unregulated hemichannel activity may induce loss of cellular homeostasis and cell death. Hemichannel activity can be regulated through several mechanisms, such as phosphorylation, divalent cations and changes in membrane potential. Additionally, it was recently postulated that redox molecules could modify hemichannels properties in vitro. However, the molecular mechanism by which redox molecules interact with hemichannels is poorly understood. In this work, we discuss the current knowledge on connexin redox regulation and we propose the hypothesis that extracellular cysteines could be important for sensing changes in redox potential. Future studies on this topic will offer new insight into hemichannel function, thereby expanding the understanding of the contribution of hemichannels to disease progression.http://journal.frontiersin.org/article/10.3389/fphys.2016.00001/ful

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

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

The more often you see an object, the easier it becomes to track it

Is it easier to track objects that you have seen repeatedly? We compared repeated blocks, where identities were the same from trial to trial, to unrepeated blocks, where identities varied. People were better in tracking objects that they saw repeatedly. We tested four hypotheses to explain this repetition benefit. First, perhaps the repeated condition benefits from consistent mapping of identities to target and distractor roles. However, the repetition benefit persisted even when both the repeated and the unrepeated conditions used consistent mapping. Second, repetition might improve the ability to recover targets that have been lost, or swapped with distractors. However, we observed a larger repetition benefit for color-color conjunctions, which do not benefit from such error recovery processes, than for unique features, which do. Furthermore, a repetition benefit was observed even in the absence of distractors. Third, perhaps repetition frees up resources by reducing memory load. However, increasing memory load by masking identities during the motion phase reduced the repetition benefit. The fourth hypothesis is that repetition facilitates identity tracking, which in turn improves location tracking. This hypothesis is consistent with all our results. Thus, our data suggest that identity and location tracking share a common resource