Chimera states in a multi-weighted neuronal network

There are multiple types of interactions among neurons, each of which has a remarkable effect on the neurons' behavior. Due to the significance of chimeras in neural processes, in this paper, we study the impact of different electrical, chemical, and ephaptic couplings on the emergence of chimera. Consequently, a multi-weighted small-world network of neurons is considered. The simultaneous effects of two and three couplings are explored on the chimera and complete synchronization. The results represent that the synchronization is achieved in very small coupling strengths in the absence of chemical synapses. In contrast, without electrical synapses, the neurons only exhibit chimera behavior. In the three-weighted network, the synchronization is enhanced for special chemical coupling strengths. The network with directed links is also examined. The general behaviors of the directed and undirected networks are the same; however, the directed links lead to lower synchronization error

Control of Spiral Waves in Reaction-Diffusion Systems Using Response Function

This thesis is motivated by the desire to understand spiral wave dynamics in reactiondiffusion systems with particular focus on the FitzHugh-Nagumo model. We attempt to control the behaviour of spiral waves using controller dynamics. Response functions characterise the behaviour of spiral waves under perturbations, and so it is natural to use these for control purposes. In this project, we consider perturbations of the FitzHugh-Nagumo equation using control functions with different support. We calculate the response functions using the adjoint linear system of the FitzHugh-Nagumo equation with 1D controller dynamics and also characterise the control functions with the smallest support function which can be used to control the system in periodic and meander regimes. We find the minimum size of the support function that the radius is comparable to the region of the non zero response function

Parameters Analysis of FitzHugh-Nagumo Model for a Reliable Simulation

International audienceDerived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model has been one of the most successful neuron / cardiac cell model. It exists many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model. The parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to pride a better simulation environment. The results showed at first that inappropriate time step and integration tolerance in numerical solution of FHN model can give some biased results which would make some publications questionable. Then the thresholds of parameters $\alpha$, $\gamma$ and $\varepsilon$ are presented. $\alpha$ controls the global dynamics of FHN. $\alpha > 0$, the cell is in refractory mode; $\alpha < 0$, the cell is excitable. $\varepsilon$ controls the main morphology of the action potential generated and has a relation with the period ($\mathrm{P} = 3.065 \times \varepsilon^{-0.8275}+4.397$). To show oscillations of relaxation with FHN, $\varepsilon$ should be smaller than $0.0085$. $\gamma$ influences barely AP, it showed linear relationship with the period and duration of action potential. Globally, when $|\alpha| \geq 0.1$, $\varepsilon < 0.0085$, there is no definite threshold for $\gamma$, but smaller values are recommended