The effects of nonlocal and reflecting connectivities have been previously investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. In this work we investigate the effect of diagonal coupling inspired by findings in brain neuron connectivity. Multi-chimera states are reported both for the simple diagonal and combined nonlocal-diagonal connectivities and we determine the range of optimal parameter regions where chimera states appear. Overall, the measures of coherence indicate that as the coupling range increases (below all-to-all coupling) the emergence of chimera states is favored and the mean phase velocity deviations between coherent and incoherent regions become more prominent. A number of novel synchronization phenomena are induced as a result of the combined connectivity. We record that for coupling strengths σ < 1 the synchronous regions have mean phase velocities lower than the asynchronous, while the opposite holds for σ > 1. In the intermediate regime, σ ∼ 1, the oscillators have common mean phase velocity (i.e., are frequency-locked) but different phases (i.e., they are phase-asynchronous). Solitary states are recorded for small values of the coupling strength, which grow into chimera states as the coupling strength increases. We determine parameter values where the combined effects of nonlocal and diagonal coupling generate chimera states with two different levels of synchronous domains mediated by asynchronous regions.

Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators whose connectivities are extracted from Magnetic Resonance Imaging (MRI) data. The numerical results demonstrate that the healthy brain presents chimera-like states where regions with high white matter concentrations in the direction connecting the two hemispheres act as the coherent domain, while the rest of the brain presents incoherent oscillations. To the contrary, in brains with destructed structures, traveling waves are produced initiated at the region where the tumor is located. These areas act as the pacemaker of the waves sweeping across the brain. The numerical simulations are performed using two neuronal models: (a) the FitzHugh-Nagumo model and (b) the leaky integrate-and-fire model. Both models give consistent results regarding the chimeralike oscillations in healthy brains and the pacemaker effect in the tumorous brains. These results are considered a starting point for further investigation in the detection of tumors with small sizes before becoming discernible on MRI recordings as well as in tumor development and evolution.

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