Activation of neuronal ensembles via controlled synchronization

"In this contribution we present the activation of neuronal ensembles of Hindmarsh-Rose neurons by controlled synchronization. The main problem consists in to impose a particular spiking-bursting behavior in all the neurons of the network. We consider a network where the neurons are in its resting state, it is desired that the neurons change their resting state to a particular behavior of activation, dictated by a neuron called the reference neuron. The goal is reached by controlling some neurons in the network controlling only the membrane potential (electrical synapse). The key feature of the present contribution is that by controlling a small number of neurons in the network a desired behavior is induced in all the neurons in the network despite its network topology. The important parameters are the control gain and the coupling strength, thus the activation of the network lays down on a compromise between the control gain and the coupling strength.

Lie algebra on synchronization of different systems: a generalized function for Hodgkin-Huxley neurons

"In this contribution two results are taken: (1) The synchronization of noiseless Hodgkin- Huxley (HH) neurons is possible from robust feedback based on Lie algebra approaches and (2) the fact that, from Lie algebra of vector fields, the generalized synchronization of different (triangular form) chaotic systems can be used to derive an explicit synchronization function. Both results are extended to derive the synchronization function in HH neurons despite this systems are not in triangular form. Thus, the Lie algebra of vectors fields permits to establish a theoretical framework for finding the synchroniza- tion function in chaotic systems in face they have different model.

Desarrollo de las úlceras en el pie diabético

Resumen: El pie diabético constituye un problema de salud pública por su alta prevalencia y sus enormes costos. Debido a esto, es necesario investigar nuevos enfoques de prevención y tratamiento de las complicaciones vasculares del pie diabético, para entender el comportamiento del padecimiento y obtener información relevante. Por tal motivo, se requiere un acercamiento multidisciplinario que ayude a evitar complicaciones vasculares en las extremidades inferiores. En esta contribución describimos como el uso de herramientas matemáticasy en particular la teoría de grafos sirven para estudiar y describir el comportamiento del desarrollo de las úlceras en el pie diabético. Los resultados muestran que es posible describir la dinámica de las úlceras en el grafo incorporando información fisiológica de las úlceras. Palabras clave: Pie diabético, grafo, úlcera

A standard microcontroller based Discrete-Time PI for controlling the motion of a DC-Gearmotor

"This paper shows how the INTEL© D8751 H microcontroller can be used to control the motion of a DC-Gearmotor. One advantage of this design is that does not require external memory RAM/EPROM to perform the control of the motor. A precision potentiometer and an analog-to-digital converter (ADC) are used to measure the motor angular position. The ADC is driven by the ALE signal from the microcontroller; therefore an external signal clock is not required. In order to implement a discrete-time PI controller and a discrete-time filter, specific libraries were designed. Moreover, other libraries based on micro C® compiler, has been modified. Finally, experimental results show a good performance of the embedded system.""Este articulo muestra como el microcontrolador D8751 H de INTEL©, puede ser utilizado para controlar el movimiento de un Moto-reductor de corriente directa. Una ventaja de este diseño es que no necesita memoria externa RAM/EPROM para controlar el motor. Para medir la posición angular del motor un potenciómetro de precisión y un convertidor analógico a digital son usados. Este ADC utiliza la señal ALE generada por el microcontrolador como señal de reloj y por lo tanto una señal externa de reloj no es necesaria. Además para poder implementar el controlador PI y el filtro digital se tuvieron que desarrollar rutinas especiales y modificar otras basadas en el compilador C®. Finalmente los resultados experimentales muestran un buen desempeño del sistema completo.

Complete Synchronization of Strictly Different Chaotic Systems

The criteria for complete synchronization of strictly different chaotic systems using feedback control are presented in this paper. Complete synchronization is achieved when all the states in the slave system are synchronous with the corresponding state in the master system. We illustrate that using a single input and single output control scheme, the synchronization of a class of strictly different systems is obtained in partial form. To overcome this problem we show that a multiple input and multiple output control scheme with an equal number of inputs and outputs than the order system is required in order to obtain the complete synchronization. This procedure is used to synchronize the Rössler and the Chen systems as an example. We also demonstrate that if the synchronization scheme considers less inputs and outputs, the partial-state synchronization is obtained

Synchronization of chaotic systems with different order

"The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is achieved in reduced order. Duffing equation is chosen as slave system whereas Chua oscillator is defined as master system. The synchronization scheme has nonlinear feedback structure. The reduced-order synchronization is attained in a practical sense, i.e., the difference e = x 3 ? x ? 1 is close to zero for all time t >~ t 0 >~ 0 , where t 0 denotes the time of the control activation.

Synchronization in Time-Varying and Evolving Complex Networks

In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples

Desarrollo de las úlceras en el pie diabético

El pie diabético constituye un problema de salud pública por su alta prevalencia y sus enormes costos. Debido a esto, es necesario investigar nuevos enfoques de prevención y tratamiento de las complicaciones vasculares del pie diabético, para entender el comportamiento del padecimiento y obtener información relevante. Por tal motivo, se requiere un acercamiento multidisciplinario que ayude a evitar complicaciones vasculares en las extremidades inferiores. En esta contribución describimos como el uso de herramientas matemáticas y en particular la teoría de grafos sirven para estudiar y describir el comportamiento del desarrollo de las úlceras en el pie diabético. Los resultados muestran que es posible describir la dinámica de las úlceras en el grafo incorporando información fisiológica de las úlceras

Bilateral teleoperation control without velocity measurements

This paper presents two controllers for a nonlinear bilateral teleoperation system that do not rely on velocity measurements. Under the reasonable assumptions that the human operator and the environment define passive maps from force to velocity, both controllers can ensure boundedness of velocities and position error. Moreover, if the human and environment forces are bounded, one of the controllers ensure velocity synchronization and the other velocity convergence to zero. Simulations, comparing the performance on free motion and interacting with a stiff wall, support the performance of the reported schemes.Postprint (published version

Exact Sinusoidal Signal Tracking on a Modified Topology of Boost and Buck-Boost Converters

This contribution presents new DC–DC Boost and Buck-Boost converter topologies to track sinusoidal signals in an exact form, that is, with zero error tracking. The proposed topology considers two DC–DC converters connected to the same load, which means that the converters are not in a cascade connection. To track the exact sinusoidal reference, the control algorithm is based on the indirect control algorithm and the harmonic balance method. The main contribution is to consider two control inputs that facilitate and permit canceling out the second harmonic generated by the nonlinearity of the model, and as a result there is a single frequency in the output. The result is such that the converters can track sinusoidal signals with exactly zero error. With this, there is a reduction in the potential negative effects on systems and equipment; some numerical results are presented to corroborate the proposal