# Alexander N PisarchikUniversidad Politécnica de Madrid | UPM · Centre for Biomedical Technology

Alexander N Pisarchik

PhD

## About

321

Publications

35,460

Reads

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5,319

Citations

Introduction

My research interests include chaos theory, synchronization, multistability, stochastic processes and intermittency, with applications to electronic, optical, and biomedical systems.

Additional affiliations

June 2013 - present

December 1999 - July 2017

April 1999 - November 1999

**Monocrom**

Position

- Consultant

Education

June 1997 - June 1997

September 1971 - June 1976

## Publications

Publications (321)

We study experimentally and numerically the dynamics of a balance platform during a short-term training. The results of experiments with sixteen untrained subjects and a developed empirical biomechanical model exhibit the coexistence of three attractors under adaptive control of multistability. During the experiments, we measure the balance bar ang...

Despite a great variety of underlying mechanisms, the overall behavior of multistable systems is fairly similar. All of them exhibit very complex dynamics due to nonlinear interactions leading to the coexistence of attractors. A particular feature of such systems is their extremely high sensitivity to initial conditions. Even a slight change in the...

Extreme multistability or the coexistence of an infinite number of coexisting attractors is an intriguing phenomenon which appears in forced, coupled, and self-reproducing systems. At the first glance, extreme multistability in a dissipative system seems rather strange because the coexistence of infinite number of states is usually attributed to a...

Many systems are composed by a large set of dynamical units that interact with each other forming complex networks demonstrating multistability. We refer the readers interested in the theory of complex networks to the following excellent articles [1–3]. The units can be either simple phase oscillators, like Kuramoto oscillators [4], or dynamical sy...

Lasers are nonlinear optical devices where multistability has been extensively studied. That is why in this book we pay special attention to multistability in lasers and devote an entire chapter to this topic. After introducing the reader to the main principles of laser dynamics, we start our consideration of laser multistability with the so-called...

We study numerically the dynamics of a system composed of two artificial neurons connected via an erbium-doped fiber laser. In our system, the laser acts as an optical synapse whose dynamics is controlled with a signal generated by a presynaptic Hindmarsh-Rose neuron, while the laser output drives a postsynaptic Hindmarsh-Rose neuron. Depending on...

We investigate the dynamics of three ring-coupled double-well Duffing oscillators modelled by fractional-
order differential equations. The analysis of time series, Fourier spectra, phase portraits, Poincaré sec-
tions, and Lyapunov exponents using the fractional order and the coupling strength as control parameters,
shows that the dynamics of such...

We systematically study the effects of synaptic plasticity in the model describing dynamics of electrically coupled neuron cells. Neurotransmission through electrical synapses plays an important role in the spike synchrony among neurons in the neural network. Synaptic plasticity is known to arise from the transjunction voltage-dependent conductance...

We tested whether changes in prestimulus neural activity predict behavioral performance (decision time and errors) during a prolonged visual task. The task was to classify ambiguous stimuli—Necker cubes; manipulating the degree of ambiguity from low ambiguity (LA) to high ambiguity (HA) changed the task difficulty. First, we assumed that the observ...

We provide compelling numerical evidence of deterministic coherence and anti-coherence resonance in small networks of unidirectional coupled chaotic Rössler oscillators in star and star-ring configurations in the presence of a small mismatch between natural frequencies of the oscillators. The resonance phenomena are found in both the normalized sta...

Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in nature, including quantum mechanics. In this paper, we propose an app...

In this paper, we used an EEG system to monitor and analyze the cortical activity of children and adults at a sensor level during cognitive tasks in the form of a Schulte table. This complex cognitive task simultaneously involves several cognitive processes and systems: visual search, working memory, and mental arithmetic. We revealed that adults f...

We propose a memristive interface consisting of two FitzHugh–Nagumo electronic neurons connected via a metal–oxide (Au/Zr/ZrO2(Y)/TiN/Ti) memristive synaptic device. We create a hardware–software complex based on a commercial data acquisition system, which records a signal generated by a presynaptic electronic neuron and transmits it to a postsynap...

The purpose of this review is to observe the current state of research on sensorimotor integration in the human brain during visual perception and subsequent decision-making under conditions of ambiguous information. Methods. This review examines the approaches of time-frequency wavelet analysis for brain activity when performing perceptual tasks,...

The development of mathematical models to describe neuronal interaction processes in the brain is a challenging task of nonlinear dynamics. Recent advances in biochemistry and neuroscience allow better understanding of biological mechanisms underlying the neuron functioning and synaptic connections between neurons. Moreover, significant progress in...

Perceptual decision-making requires transforming sensory information into decisions. An ambiguity of sensory input affects perceptual decisions inducing specific time-frequency patterns on EEG (electroencephalogram) signals. This paper uses a wavelet-based method to analyze how ambiguity affects EEG features during a perceptual decision-making task...

We propose a hybrid memristve neuromorphic system for stimulating hippocampus regions bypassing damaged areas. Synaptic plasticity properties of the system allow close-loop adaptive control of neural dynamics. We implement the simplest version of this system which consists of two neuron-like generators coupled by a memristive device, and two fiber-...

We study dynamics of a ring of three unidirectionally coupled double-well Duffing oscillators for three different values of the damping coefficient: fixed dumping, proportional to time, and inversely proportional to time. The dynamics in all cases is analyzed through time series, Fourier and Hilbert transforms, Poincar\'e sections, as well as bifur...

Brain-computer interfaces (BCIs) development is closely related to physics. In this paper, we review the physical principles of BCIs, and underlying novel approaches for registration, analysis, and control of brain activity. We analyse recent advances in BCI studies focusing on their applications for (i) controlling the movement of robots and exosk...

The dynamics of memristive device in response to neuron-like signals and coupling electronic neurons via memristive device has been investigated theoretically and experimentally. The simplest experimental system consists of electronic circuit based on the FitzHugh-Nagumo model and metal-oxide memristive device. The hardware-software complex based o...

Extreme multistability is the coexistence of a large number of attractors which can be reached by varying initial conditions. In this paper we show how this fascinating phenomenon can be used for secure communication. The main advantage of the communication system based on extreme multistability over a conventional chaos-based communication system...

In this article, a beam within a ring phase conjugated laser is described by means of a Van der Pol bidimensional dynamic map using an ABCD matrix approach. Explicit expressions for the intracavity chaos-generating matrix elements were obtained; furthermore, computer calculations for different values of Van der Pol map's parameters were made. The r...

The analysis of neurophysiological data using the two most widely used open-source MATLAB toolboxes, FieldTrip and Brainstorm, validates our hypothesis about the correlation between event-related coherence in the visual cortex and neuronal noise. The analyzed data were obtained from magnetoencephalography (MEG) experiments based on visual perceptio...

This interdisciplinary book argues that the economy has an underlying non-linear structure and that business cycles are endogenous, which allows a greater explanatory power with respect to the traditional assumption that dynamics are stochastic and shocks are exogenous.
The first part of this work is formal-methodological and provides the mathemati...

In this study, voluntary and involuntary visual attention focused on different interpretations of a bistable image, were investigated using magnetoencephalography (MEG). A Necker cube with sinusoidally modulated pixels' intensity in the front and rear faces with frequencies 6.67 Hz (60/9) and 8.57 Hz (60/7), respectively, was presented to 12 health...

Piecewise functions are common in the mathematical modelling of various systems, including mechanical and electronic devices, demography and economy, and robotics and control equipment. Many studies of piecewise systems are addressed towards the analysis of their solutions using well-structured traditional and non-conventional techniques. In partic...

A problem of mathematical modeling and analysis of complex oscillatory behavior in coupled nonlinear stochastic systems is considered. We study stochastic bifurcations and transitions between in-phase and anti-phase dynamics in two coupled map-based neural oscillators with regular and chaotic attractors. Interesting dynamical regimes of isolated an...

We present a novel integration technology for replacing damaged microcircuits in the rat brain with electronic neuronal networks. This technology will allow simulating important brain functions, such as memory, through the adaptive stimulating effects of neural interfaces at cellular and neuronal network levels. The proposed system includes electro...

A complex network of bistable Hodgkin-Huxley (HH) neurons with excitatory coupling can exhibit a partially spiking chimera behavior. We propose to use this chimera-like state for classification of the entering stimulus amplitude in the neural network with coexisting resting and spiking states. Due to different additive noise applied to each neuron...

UNSTRUCTURED
Voluntary and involuntary visual attention in different interpretations of a bistable image was investigated using magnetoencephalography (MEG). A Necker cube with sinusoidally modulated pixels' intensity in the front and rear faces with frequencies 6.67 Hz (60/9) and 8.57 Hz (60/7), respectively, was presented to twelve healthy volunt...

We propose an experimental arrangement to increase pulse energy in the array of erbium-doped fiber lasers (EDFLs). The experimental setup consists of three coupled periodically modulated multistable EDFLs; one master laser and two slave lasers. The master laser is tuned to the coexisting attractor with the largest peak amplitude and synchronizes th...

Decision-making requires the accumulation of sensory evidence. However, in everyday life, sensory information is often ambiguous and contains decision-irrelevant features. This means that the brain must disambiguate sensory input and extract decision-relevant features. Sensory information processing and decision-making represent two subsequent stag...

The transition from asynchronous dynamics to generalized chaotic synchronization and then to completely synchronous dynamics is known to be accompanied by on-off intermittency. We show that there is another (second) type of the transition called jump intermittency which occurs near the boundary of generalized synchronization in chaotic systems with...

We study transitions from regular to chaotic dynamics and back of a ring of three map-based neurons with parameter mismatch. First, we consider the case when each neuron being isolated is in a stable equilibrium and show that an increase in the coupling strength can lead to chaotic dynamics following a quasiperiodic behavior. Then, we consider the...

We study the emergence of synchronization in the network motif of three bistable Duffing oscillators coupled in all possible configurations. The equation of motion is derived for every configuration. For each motif, we vary initial conditions of every oscillator and calculate the bi-furcation diagram as a function of the coupling strength. We find...

We develop an advanced model of bistable perception based on the interplay of noise and adaptation. The model describes the decision-making process in the brain consisting in involuntary switches between perceptual states. We study the effects of noise and the stimulus duty cycle on the dominance of a particular externally biased perceptual state....

A review of physical and mathematical methods for reconstructing the functional networks of the brain based on recorded brain activity is presented. Various methods are considered, as are their advantages and disadvantages and limitations of the application. Problems applying the theory of complex networks to reconstructed functional networks of th...

We study a stochastic spatially extended population model with diffusion, where we find the coexistence of multiple non-homogeneous spatial structures in the areas of Turing instability. Transient processes of pattern generation are studied in detail. We also investigate the influence of random perturbations on the pattern formation. Scenarios of n...

Sensor-level human brain activity is studied during real and imaginary motor execution using functional near-infrared spectroscopy (fNIRS). Blood oxygenation and deoxygenation spatial dynamics exhibit pronounced hemispheric lateralization when performing motor tasks with the left and right hands. This fact allowed us to reveal biomarkers of hemodyn...

Brain optimally utilizes resources to resist mental fatigue during the prolonged period of cognitive activity. Neural mechanisms underlying long-term cognitive performance remain unknown. We show that during the 40-minutes visual stimuli classification task, subjects improve behavioral performance in terms of response time and correctness. We obser...

SISTEMA DE COMUNICACIÓN SEGURA BASADO EN MULTI-ESTABILIDAD.
Se divulga un sistema de comunicación segura basado en multi-estabilidad conformado por emisor/receptor basados en osciladores caóticos multi-estables y dos canales de comunicación público/privado. El privado permite sincronizar los osciladores de emisor y receptor. Conmutadores caóticos i...

We introduce a method for measuring human attention when performing a visual task consisting in different interpretations of a bistable image. The Necker cube with flickering faces was presented to nine conditionally healthy volunteers. The pixels intensity in the front and rear cube faces were modulated by a sinusoidal signal with 6.67-Hz (60/9) a...

We study noise-induced intermittency in a synergetic model of two coupled oscillators with asymmetric nonlinear coupling. This model was previously used to simulate visual perception of ambiguous images. We show that additive noise induces preference for one of the coexisting unstable steady states. When the noise intensity exceeds a certain thresh...

Neuronal brain network is a distributed computing system, whose architecture is dynamically adjusted to provide optimal performance of sensory processing. A small amount of visual information needed effortlessly be processed, activates neural activity in occipital and parietal areas. Conversely, a visual task which requires sustained attention to p...

The knowledge of the mechanisms of motor imagery (MI) is very important for the development of braincomputer interfaces. Depending on neurophysiological cortical activity, MI can be divided into two categories: visual imagery (VI) and kinesthetic imagery (KI). Our magnetoencephalography (MEG) experiments with ten untrained subjects provided evidenc...

A nonlinear dynamical model of two coupled neurons based on the Rulkov map is considered. Variability analysis of corporate dynamics depending on the type of activity of separated neurons and strength of coupling is performed. Transitions between stationary, periodic, quasiperiodic, and chaotic regimes of this neuron system are studied. Additional...

We study the influence of random noise on the two-dimensional model of enzymatic reaction. The model demonstrates high non-uniformity of deterministic phase portrait and sensitivity to parameters variations. A new dynamical phenomenon of the noise-induced generation of phantom attractor is found in this biochemical model forced by multiplicative ra...

Topology of a functional brain multilayer network is dynamically adjusted to provide optimal performance during accomplishing cognitive tasks, including sensory information processing. Functional connectivity between brain regions is achieved in terms of correlation or synchronization inference in recorded signals of neuronal activity. The promisin...

UNSTRUCTURED
We comment on the paper “An integrated brain-machine interface platform with thousands of channels” by Elon Musk & Neuralink.

Machine learning is a promising approach for electroencephalographic (EEG) trials classification. Its efficiency is largely determined by the feature extraction and selection techniques reducing the dimensionality of input data. Dimensionality reduction is usually implemented via the mathematical approaches (e.g., principal component analysis, line...

Behavioral experiments evidence that attention is not maintained at a constant level, but fluctuates with time. Recent studies associate such fluctuations with dynamics of attention-related cortical networks, however the exact mechanism remains unclear. To address this issue, we consider functional neuronal interactions during the accomplishment of...