Impact of Lévy noise on spiral waves in a lattice of Chialvo neuron map

We aim to explore the features of destroying the spiral wave regime in a lattice network of Chialvo neurons by applying external noise with different statistical characteristics. Chialvo neurons are represented with a two-dimensional recurrence map. The lattice of neurons under study observed with random initial conditions and with special initial conditions for local and nonlocal coupling. We consider a detailed two-parameter plot in the plane of coupling strength — distribution width of Lévy process which revealed that the existence of spiral waves are dependent on the network and noise parameters. We examine how coupling strength and range parameters influence on the spiral wave dynamics in a coupled lattice system. Increasing the coupling range enlarges the region where spiral waves can exist. Additionally we show that the destruction of spiral waves is achievable with a certain threshold of the distribution width parameter value depending on the noise stability parameter value and the noise asymmetry parameter value. A decrease in the noise stability parameter as well as in the noise asymmetry parameter decreases the threshold value. We show that the influence of Lévy noise on spiral waves in the lattice of Chialvo neurons results in a transition to target waves that are more stable than in the case of transition for random initial conditions to target waves without noise. Finally, we have found that the noise could cause the lattice to switch between various spiral-like regimes as time passes.