# Ibere Luiz CaldasUniversity of São Paulo | USP · Department of Applied Physics

Ibere Luiz Caldas

PhD

## About

455

Publications

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4,000

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Citations since 2017

Introduction

Theory of chaos applied to plasma physics, mechanical systems, electric circuits, oscillator networks, neuronal networks. Plasma turbulence and transport.

## Publications

Publications (455)

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories with great accuracy. Their usage arises in many fields, including celeste mechanics, plasma physics, chemistry...

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection–collision sequences and shearless invariant curves that act as transport barriers in the phase space. Although reported in numerical investigati...

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories with great accuracy. Their usage arises in many fields, including celeste mechanics, plasma physics, chemistry...

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting re...

The ${\bf E}\times{\bf B}$ drift motion of particles in tokamaks provides valuable information on the turbulence-driven anomalous transport. One of the characteristic features of the drift motion dynamics is the presence of chaotic orbits for which the guiding center can experience large-scale drifts. If one or more exits are placed within that cha...

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all t...

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dy-namical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all...

Synaptic time delays and plasticity are intrinsic characteristics present in real neuronal networks, and the interplay between both can promote complex dynamics in the brain. In this work, we build connected plastic subnetworks of Hodgkin-Huxley neurons where the subnetworks are composed of excitatory neurons and the connectivity modifications foll...

We study the time delay in the synaptic conductance for suppression of spike synchronisation in a random network of Hodgkin–Huxley neurons coupled by means of chemical synapses. In the first part, we examine in detail how the time delay acts over the network during the synchronised and desynchronised neuronal activities. We observe a relation betwe...

In this work, we consider a phenomenological two-dimensional discrete model coupled in a structure of a clustered network to investigate the suppression of neuronal synchronization in a complex network. We constructed a network according to a weighted human connectivity matrix and an adjacency matrix that carries small-world properties. The couplin...

In this work, we show that a finite-time recurrence analysis of different chaotic trajectories in two-dimensional non-linear Hamiltonian systems provides useful prior knowledge of their dynamical behavior. By defining an ensemble of initial conditions, evolving them until a given maximum iteration time, and computing the recurrence rate of each orb...

Intrinsically coupled nonlinear systems typically present different oscillating components that exchange energy among themselves. A paradigmatic example is the spring pendulum, for which we identify spring, pendulum, and coupled oscillations. We propose a new approach that properly accounts for the nonlinear coupling, and allows the analysis of ene...

Chimera states are spatiotemporal patterns in which distinct dynamics coexist, such as synchronous and asynchronous patterns. In this work, we study the effect of spike timing-dependent plasticity (STDP) on the emergence of chimera states. We consider a regular network of coupled adaptive exponential integrate-and-fire neurons, where all connection...

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection-collision sequences and shearless invariant curves that act as transport barriers in the phase space. Although reported in numerical investigati...

The L-H transition leads to a substantial reduction in transport levels in tokamaks and stellarators, improving the plasma confinement in such devices. After the transition, the plasma is in a high-confinement regime characterized by steep density and temperature gradients, with a large radial electric field at the plasma edge. In this paper, we sh...

The transport of particles in the phase space is investigated in the Fermi-Ulam model. The system consists of a particle confined to move within two rigid walls with which it collides. One is fixed and the other is periodically moving in time. In this work we investigate, for this model, the location of invariant curves that separate chaotic areas...

In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: $i) unlimited doses, (ii) limited doses into susceptible individuals, and (iii) limited doses randomly distributed...

Intrinsically coupled nonlinear systems present different oscillating components that exchange energy among themselves. A paradigmatic example is the spring pendulum, which displays spring, pendulum, and coupled oscillations. We analyze the energy exchanges among the oscillations, and obtain that it is enhanced for chaotic orbits. Moreover, the hig...

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-center trajectories of plasma particles undergoing ExB drift motion, considering that the electric field has a stationary nonmonotonic radial profile and an...

For some discharge configurations in tokamaks, transport barriers reduce particle transport, improving plasma confinement. In this context, a model has been applied to describe the turbulent transport by drift waves, attributing this transport to ExB chaotic drift orbits. In the present work we use this model to investigate the influence of magneti...

A detailed resource to data analysis shows that the widely known van Hoven and Derfler–Simonen laboratory results are far from reasonable agreement with the standard Bohm–Gross dispersion relation. We provide an extension of the usual notion of a polytropic index to non-Boltzmann–Gibbs statistics. Such an extension allows for the deduction of an eq...

Shearless barrier improves the plasma confinement and can be created by the application of a bias. Previously, they were identified with a 2D map of charged particle motion in one drift mode. Now, we add a second drift mode and derive a 3D map. By fixing the parameters related to the first mode and varying the second mode amplitude, we show that th...

We study the time delay in the synaptic conductance for suppression of spike synchronisation in a random network of Hodgkin Huxley neurons coupled by means of chemical synapses. In the first part, we examine in detail how the time delay acts over the network during the synchronised and desynchronised neuronal activities. We observe a relation betwe...

We investigate the turbulence level dependence on plasma profiles in experiments in Texas Helimak, a toroidal basic plasma device, with long stable electron cyclotron resonant heating (ECRH) discharges and great flexibility to alter the equilibrium magnetic field. A large set of Langmuir probes is used to obtain the turbulence level and also the pl...

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional “soft” billiard, classically modeled from an optical lattice Hamiltonian system, is used to study diffusion transitions under variation of the control parameters. Su...

In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: (i) unlimited doses, (ii) limited doses into susceptible individuals, and (iii) limited doses randomly distributed...

Neuronal spike variability is a statistical property associated with the noise environment. Considering a linearised Hodgkin–Huxley model, we investigate how large spike variability can be induced in a typical stellate cell when submitted to constant and noise current amplitudes. For low noise current, we observe only periodic firing (active) or si...

The resonant interaction between charged particles and electromagnetic waves in plasmas is a very efficient mechanism for particle acceleration. In general, the acceleration process depends on the wave amplitude. For small amplitude waves, the energy transferred to the particles is not enough to produce a considerable amount of acceleration. On the...

The neuron dynamics is highly susceptible to variations in its current input. In this work, we study the dynamics of uncoupled and random coupled Hodgkin Huxley neurons under an external current with constant or pulsed amplitude. The profile of these pulse perturbations are considered as periodic, random, and a mix between these two types. For unco...

Mathematical modeling is an important tool to analyze impacts and plan to mitigate epidemics in communities. In order to estimate the impact of control measures in a second wave of infections, we analyze the SEIR epidemic model based on stochastic cellular automata. The control measure is based on one of the key strategies to control the epidemic,...

One of the main consequences of the complex hierarchical structure of chaotic regions and stability islands in the phase space of a typical nonlinear Hamiltonian system is the phenomenon of stickiness. The chaotic orbits that approach an island are trapped in its neighborhood for arbitrarily long times, in which the orbits behave similarly as quasi...

Osciladores de fase são sistemas dinâmicos dissipativos com aporte externo de energia, e matematicamente caracterizados pela presença de ciclos-limite, ao longo dos quais a dinâmica pode ser descrita por um ângulo de fase. No presente artigo, consideramos fenômenos de sincronização num sistema de muitos osciladores de fase acoplados. Adotamos uma d...

Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. Previous researchers have argued which epileptic and normal neuronal activity are support by the same physiological structure. However, to understand how neuronal systems transit between these regimes is a wide ques...

Understanding how the brain synchronizes is a fundamental question in neuroscience. The main types of synchronization found between the brain regions are phase, anti-phase, and shift-phase. In phase synchronization, neurons of two regions fire at the same time. This type of synchronization has been observed, for instance, during memory, cognition,...

Insulin is a hormone that plays a crucial role in controlling the transport of glucose from the blood to inside the cells. In the pancreas, the insulin is secreted by the 'beta' cells, according to the blood glucose concentration, and the interaction of insulin with the glucose is responsible for providing energy to the cells. In this work, we stud...

Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system’s domain. The motion described by such escape orbits before crossing the escape threshold can be understood as a transient behavior. In this work, we introduce a numerical method to visually illustrate and quant...

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional ``soft'' billiard, classically modeled from an optical lattice hamiltonian system, is used to study diffusion transitions with the control parameters variation. Sudd...

Periodic orbits are fundamental to nonlinear systems. We investigate periodic orbits for a dissipative mapping, derived from a prototype model of a non-linear driven oscillator with fast relaxation and a limit cycle. We show numerically the exponential growth of periodic orbits quantity and provide an analytical bound for such growth rate, by makin...

We provide a formulation that describes the propagation of solitons in a nondissipative, nonmagnetic plasma, which does not depend on the particular electron density distribution considered. The Poisson equation in the plasma sheath is expressed in terms of the Mach number for ions entering the sheath from the plasma and of a natural scale for the...

Barriers have been identified in magnetically confined plasmas reducing the particle transport and improving the confinement. One of them, the primary shearless barriers are associated to extrema of non-monotonic plasma profiles. Previously, we identified these barriers in a model described by a map that allows the integration of charged particles...

We analyze nonlinear aspects of the self-consistent wave–particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N=1) is coupled with one...

Barriers have been identified in magnetically confined plasmas by reducing the particle transport and improving the confinement. One of them, the primary shearless barriers, is associated with extrema of non-monotonic plasma profiles. Previously, we identified these barriers in a model described by a map that allows the integration of charged parti...

Oscillatory activities in the brain, detected by electroencephalograms, have identified synchronization patterns. These synchronized activities in neurons are related to cognitive processes. Additionally, experimental research studies on neuronal rhythms have shown synchronous oscillations in brain disorders. Mathematical modeling of networks has b...

Brain tumours are masses of abnormal cells that can grow in an uncontrolled way in the brain. There are different types of malignant brain tumours. Gliomas are malignant brain tumours that grow from glial cells and are identified as astrocytoma, oligodendroglioma, and ependymoma. We study a mathematical model that describes glia-neuron interaction,...

Understanding how the brain synchronizes is a fundamental question in neuroscience. The main types of synchronization found between the brain regions are phase, anti-phase, and shift-phase. In phase synchronization, neurons of two regions fire at the same time. This type of synchronization has been observed, for instance, during memory, cognition,...

We provide a non-adiabatic equation of state of a space plasma based on the kappa distribution. Our formulation generalizes the polytropic gamma index. An analytic expression is deduced for gamma. Then, the equation of state is derived. The model is applied to describe the electron solar wind in the Earth’s magnetopause. A relationship between the...

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov–Taylor Standard Map. We show that trajectories started from special initial conditions, close to unstable periodic orbits, exhibit sub-diffusion due to stickiness, and can be modeled as a continuous-time random walk. Additionally, we choose a variant of the Ulam met...

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious diseases. In other words, mathematical model simulation can be used to analyse the dynamics of infectious diseases, ai...

The influence of temperature on interfacial fluid slip, as measured by molecular dynamics simulations of a Couette flow comprising a Lennard–Jones fluid and rigid crystalline walls, is examined as a function of the fluid–solid interaction strength. Two different types of thermal behavior are observed, namely, the slippery and sticky cases. The firs...

We consider a 4 meters long traveling wave tube (TWT) that presents an upgraded slow wave structure. We analyze linear and nonlinear phenomena due to the beam-wave interaction in the device, e.g. beam modulation, and wave growth and saturation.

The influence of temperature on interfacial fluid slip, as measured by molecular-dynamics simulations of a Couette flow comprising a Lennard-Jones fluid and rigid crystalline walls, is examined as a function of the fluid-solid interaction strength. As a result, two completely different thermal behaviors are observed, namely, the slippery and sticky...

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mat...

One of the most fundamental questions in the field of neuroscience is the emergence of synchronous behaviour in the brain, such as phase, anti-phase, and shift-phase synchronisation. In this work, we investigate how the connectivity between brain areas can influence the phase angle and the neuronal synchronisation. To do this, we consider brain are...

A chaotic saddle is a common nonattracting chaotic set well known for generating finite-Time chaotic behavior in low and high-dimensional systems. In general, dynamical systems possessing chaotic saddles in their state-space exhibit irregular behavior with duration lengths following an exponential distribution. However, when these systems are coupl...

Much work has been done to investigate social jetlag, a misalignment between the biological clock and the social agenda, related to exposition to dirent light inputs, that causes several health issues. To investigate synchronization and attractors due to a sequence of light inputs, we introduce an extension of a model, previously used to describe j...

The turbulence of magnetically confined plasmas usually presents high-density pulses with short duration known as bursts. In the Texas Helimak, it is possible to suppress bursts in a broader region by applying a negative electrostatic bias. However, an almost unchanged burst rate persists in a region far from the location where bias is applied. We...

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mat...

An equation of state of a gas of electrons of dense matter at high pressure is proposed with basis on the Thomas-Fermi theory by taking into account a modification of an adiabatic relation. The formulation is applied to describe the behavior of the concentrations of alkali metals subjected to pressure excesses up to 100,000kgf/cm2. The outcomes sug...

The routes to chaos play an important role in predictions about the transitions from regular to irregular behavior in nonlinear dynamical systems, such as electrical oscillators, chemical reactions, biomedical rhythms, and nonlinear wave coupling. Of special interest are dissipative systems obtained by adding a dissipation term in a given Hamiltoni...

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious diseases. In other words, mathematical model simulation can be used to analyse the dynamics of infectious diseases, ai...

The study could help upgrade satellite communications equipment.
A paper on research conducted by Meirielen Caetano de Sousa, postdoctoral fellow at the University of São Paulo’s Physics Institute (IF-USP) in Brazil, is highlighted as Editor’s Pick in the September issue of Physics of Plasmas, published by the American Institute of Physics with th...

Periodic orbits are fundamental to understand the dynamics of nonlinear systems. In this work, we focus on two aspects of interest regarding periodic orbits, in the context of a dissipative mapping, derived from a prototype model of a non-linear driven oscillator with fast relaxation and a limit cycle. For this map, we show numerically the exponent...

Much work has been done to investigate social jetlag, a misalignment between the biological clock and the social agenda caused by exposition to different light inputs, that causes several health issues. To investigate synchronization and attractors due to a sequence of light inputs, we introduce an extension of a model, previously used to describe...

Brain tumours are masses of abnormal cells that can grow in an uncontrolled way in the brain. There are different types of malignant brain tumours. Gliomas are malignant brain tumours that grow from glial cells and are identified as astrocytoma, oligodendroglioma, and ependymoma. We study a mathematical model that describes glia-neuron interaction,...

We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N = 1) is coupled with on...

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time Random Walk model and connected to the theoretical background for anomalous diffusion. Additionally, we choose a...

In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point L1 is always open, but the orb...

A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronization. Here, we build a random network with adaptive exponential integrate-and-fire neurons c...

Chimera states are spatial patterns in which coherent and incoherent patterns coexist. It was reported that small populations of coupled oscillators can exhibit chimera with transient nature. This spatial coexistence has been observed in various network topologies of coupled systems, such as coupled pendula, coupled chemical oscillators, and neuron...