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Papers by Paulo Protachevicz

Physica A: Statistical Mechanics and its Applications, 2022

Cognitive Neurodynamics, 2022

Chaos, Solitons & Fractals, 2022

$Research paper thumbnail of Spiral wave chimera states in regular and fractal neuronal networks$

Journal of Physics: Complexity, 2020

Chimera states are spatial patterns in which coherent and incoherent patterns coexist. It was rep... more 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 neuronal networks. In this work, we build two-dimensional neuronal networks with regular and fractal topologies to study chimera states. In the regular network, we consider a coupling between the nearest neighbours neurons, while the fractal network is constructed according to the square Cantor set. Our networks are composed of coupled adaptive exponential integrate-and-fire neurons, that can exhibit spike or burst activities. Depending on the parameters, we find spiral wave chimeras in both regular and fractal networks. The spiral wave chimeras arise for different values of the intensity of the excitatory synaptic conductance. In our simulation...

arXiv: Neurons and Cognition, 2020

Noise appears in the brain due to various sources, such as ionic channel fluctuations and synapti... more Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to model firing patterns of neurons subject to noise. In this work, we consider perturbing noise in the adaptive exponential integrate-and-fire (AEIF) neuron. The AEIF is a two- dimensional model that describes different neuronal firing patterns by varying its parameters. Noise is added in the equation related to the membrane potential. We show that a noise current can induce continuous and noncontinuous transitions in neuronal interspike intervals. Moreover, we show that the noncontinuous transition occurs mainly for parameters close to the border between tonic spiking and burst activities of the neuron without noise

The brain can display self-sustained activity (SSA), which is the persistent firing of neurons in... more The brain can display self-sustained activity (SSA), which is the persistent firing of neurons in the absence of external stimuli. This spontaneous activity shows low neuronal firing rates and is observed in diverse in vitro and in vivo situations. In this work, we study the influence of excitatory/inhibitory balance, connection density, and network size on the self-sustained activity of a neuronal network model. We build a random network of adaptive exponential integrate-and-fire (AdEx) neuron models connected through inhibitory and excitatory chemical synapses. The AdEx model mimics several behaviours of biological neurons, such as spike initiation, adaptation, and bursting patterns. In an excitation/inhibition balanced state, if the mean connection degree (K) is fixed, the firing rate does not depend on the network size (N), whereas for fixed N, the firing rate decreases when K increases. However, for large K, SSA states can appear only for large N. We show the existence of SSA s...

Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide an... more Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be weakened by the cancer. One type of cancer treatment is chemotherapy, which uses drugs to kill cancer cells. Clinical, experimental, and theoretical research has been developed to understand the dynamics of cancerous cells with chemotherapy treatment, as well as the interaction between tumour growth and immune system. We study a mathematical model that describes the cancer growth, immune system response, and chemotherapeutic agents. The immune system is composed of resting cells that are converted to hunting cells to combat the cancer. In this work, we consider drug sensitive and resistant cancer cells. We show that the tumour growth can be controlled not only by means of different chemotherapy protocols, but also by the immune system that attacks both s...

Physica A: Statistical Mechanics and its Applications, 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019

Apresenta-se neste trabalho, um estudo da influência da perda de neurônios na taxa de disparos ne... more Apresenta-se neste trabalho, um estudo da influência da perda de neurônios na taxa de disparos neuronais. Para tal estudo foi elaborado um modelo de autômato celular que simula a proliferação de células cancerígenas em um tecido cerebral e a morte de neurônios devido a falta de assistência das células que lhes dão suporte nutricional e funcional. Por meio do modelo analisou-se a taxa de disparos neuronais considerando diferentes valores de perturbação externa e probabilidades de proliferação de células cancerígenas. Com este trabalho conclui-se que a presença de proliferação não controlada de células, diminui a taxa de disparos neuronais.

Communications in Nonlinear Science and Numerical Simulation, 2021

Neural Networks

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-an... more We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the inter-spike interval and the calculation of the order parameter. Moreover, we verify the robustness of synchronisation by applying an external perturbation to each neuron. The simulations show that bursting synchronisation is more robust than spike synchronisation.

One of the most fundamental questions in the field of neuroscience is the emergence of synchronou... more 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 areas connected by means of excitatory and inhibitory synapses, in which the neuron dynamics is given by the adaptive exponential integrate-and-fire model. Our simulations suggest that excitatory and inhibitory connections from one area to another play a crucial role in the emergence of these types of synchronisation. Thus, in the case of unidirectional interaction, we observe that the phase angles of the neurons in the receiver area depend on the excitatory and inhibitory synapses which arrive from the sender area. Moreover, when the neurons in the sender area are synchronised, the phase angle variability of the receiver area can be reduced ...

Communications in Nonlinear Science and Numerical Simulation