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The present work is devoted to the detailed quantification of the transitionfrom spiral waves to spiral wave chimeras in a network of self-sustainedoscillators with two-dimensional geometry. The basic elements of the networksare the van der Pol oscillator and the FitzHugh-Nagumo neuron. Both models arein the regime of relaxation oscillations. We analyze the regime by using theindices of local sensitivity which enables us to evaluate the sensitivity ofeach individual oscillator at finite time. Spi-ral waves are observed in bothlattices when the interaction between elements have the local character. Thedynamics of all the elements is regular. There are no high-sensitive regions.We have discovered that when the coupling becomes nonlocal, the features of thesystems significantly changes. The oscillation regime of the spiral wave centerelement switches to chaotic one. Besides this, a region with high sensitivityoccurs around this oscillator. Moreover, we show that the latter expands inspace with elongation of the coupling range. As a result, an incoherencecluster of the spiral wave chimera is formed exactly within this high-sensitivearea. Formation of this cluster is accompanied by the sharp increase in valuesof the maximal Lyapunov exponent to the positive region. Furthermore, weexplore that the system can even switch to hyperchaotic regime, when severalLyapunov exponents becomes positive.

Quantifying the transition from spiral waves to spiral wave chimeras in a lattice of self-sustained oscillators