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.

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.

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.

Stabilization of a class of biomedical systems via stability preservation

"We present a method for stabilization of a class of nonlinear systems. The notion of stability preservation is exploited to prove that a transformation allows to find a stabilizer. The nonlinear systems have uncontrollable linearized system. From this fact, we propose a method that departs from a controllable linearized system to a linear transformation. The linear transformation allows to take the uncontrolled system preserving the stability properties of the controlled one. Thus, the resulting controller is able to stabilize biomedical systems. Type I diabetes mellitus and HIV-I diseases are used to show the potential of method. Numerical simulations for this case illustrate the performance of closed loop approach.

Una aproximación algebraica de observabilidad para un sistema de diabetes mínimo

"La observabilidad de estados mediante la disponibilidad de un conjunto de entradas y salidas es un tema que, en concepto, es relativamente simple y como es sabido, para sistemas lineales está satisfactoriamente estudiado. Sin embargo para sistemas no lineales, la determinación de la observabilidad se dificulta dada la complejidad implícita de este tipo de sistemas. Esta complejidad puede deberse a retardos , sistemas de alto orden y respuestas inesperadas a acciones de control. Sin embargo, la evaluación de observabilidad es fundamental para el diseño de estimadores, identificación y control de sistemas. En el presente trabajo se emplean conceptos de álgebra diferencial, para demostrar que cierta clase de modelo mínimo de diabetes puede clasificarse como sistema diferencialmente plano y que la estimación de concentraciones de insulina a través de mediciones de glucosa en sangre es teóricamente factible empleando metodología alterna, lo cual la convierte en relevante para los estudios de ingeniería biomédica.

Multiscroll attractors by switching systems

"In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable "one-spiral" trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.

Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator

"We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-KorosNoyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.