Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: Fundação Araucária, EPSRC-EP/I032606/1 and CNPq, CAPES and Science Without Borders Program Process nos. 17656125, 99999.010583/2013-00 and 245377/2012-3.Peer reviewedPreprin

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

This work was possible by partial financial support from the following Brazilian government agencies: CNPq (154705/2016-0, 311467/2014-8), CAPES, Fundacao Araucaria, and Sao Paulo Research Foundation (processes FAPESP 2011/19296-1, 2015/07311-7, 2016/16148-5, 2016/23398-8, 2015/50122-0). Research supported by grant 2015/50122-0 Sao Paulo Research Foundation (FAPESP) and DFG-IRTG 1740/2.Peer reviewedPostprin

Spike-burst chimera states in an adaptive exponential integrate-and-fire neuronal network

We wish to acknowledge the support from Fundação Araucária, CNPq (Grant No. 150701/2018-7), CAPES, and FAPESP (Grant Nos. 2015/07311-7, 2018/03211-6, and 2017/18977-1).Peer reviewedPublisher PD

Influence of Delayed Conductance on Neuronal Synchronization

In the brain, the excitation-inhibition balance prevents abnormal synchronous behavior. However, known synaptic conductance intensity can be insufficient to account for the undesired synchronization. Due to this fact, we consider time delay in excitatory and inhibitory conductances and study its effect on the neuronal synchronization. In this work, we build a neuronal network composed of adaptive integrate-and-fire neurons coupled by means of delayed conductances. We observe that the time delay in the excitatory and inhibitory conductivities can alter both the state of the collective behavior (synchronous or desynchronous) and its type (spike or burst). For the weak coupling regime, we find that synchronization appears associated with neurons behaving with extremes highest and lowest mean firing frequency, in contrast to when desynchronization is present when neurons do not exhibit extreme values for the firing frequency. Synchronization can also be characterized by neurons presenting either the highest or the lowest levels in the mean synaptic current. For the strong coupling, synchronous burst activities can occur for delays in the inhibitory conductivity. For approximately equal-length delays in the excitatory and inhibitory conductances, desynchronous spikes activities are identified for both weak and strong coupling regimes. Therefore, our results show that not only the conductance intensity, but also short delays in the inhibitory conductance are relevant to avoid abnormal neuronal synchronization.Peer Reviewe

Inference of topology and the nature of synapses, and the flow of information in neuronal networks

ACKNOWLEDGEMENTS CAPES, DFG-IRTG 1740/2, Fundacao Araucaria, Newton Fund, CNPq (154705/2016-0, 311467/2014-8), FAPESP (2011/19296-1, 2015/07311-7, 2016/16148-5, 2016/23398-8, 2015/50122-0), EPSRC-EP/I032606.Peer reviewedPublisher PD

Bistable Firing Pattern in a Neural Network Model

Excessively high, neural synchronization has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronization mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronization in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronization originating from a pattern of desynchronized spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronization, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronization by applying a small-amplitude external current on > 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behavior, but more importantly, it can be used as a means to reduce abnormal synchronization and thus, control or treat effectively epileptic seizures.Peer Reviewe

Fractional dynamics and recurrence analysis in cancer model

In this work, we analyze the effects of fractional derivatives in the chaotic dynamics of a cancer model. We begin by studying the dynamics of a standard model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by means of the bifurcation diagram, Lyapunov exponents, and recurrence quantification analysis (RQA), such as the recurrence rate (RR), the determinism (DET), and the recurrence time entropy (RTE). We find a high correlation coefficient between the Lyapunov exponents and RTE. Our simulations suggest that the tumor growth parameter ($\rho_1$) is associated with a chaotic regime. Our results suggest a high correlation between the largest Lyapunov exponents and RTE. After understanding the dynamics of the model in the standard formulation, we extend our results by considering fractional operators. We fix the parameters in the chaotic regime and investigate the effects of the fractional order. We demonstrate how fractional dynamics can be properly characterized using RQA measures, which offer the advantage of not requiring knowledge of the fractional Jacobian matrix. We find that the chaotic motion is suppressed as $\alpha$ decreases, and the system becomes periodic for $\alpha \lessapprox 0.9966$. We observe limit cycles for $\alpha \in (0.9966,0.899)$ and fixed points for $\alpha<0.899$. The fixed point is determined analytically for the considered parameters. Finally, we discover that these dynamics are separated by an exponential relationship between $\alpha$ and $\rho_1$. Also, the transition depends on a supper transient which obeys the same relationship