We analyse the dynamics of the improved discretised version of the well known Izhikevich
neuron model under the action of external electromagnetic field. It is found that the improved …

In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps of
three or higher dimensions. The “torus” is represented by a closed loop in discrete time …

We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled
nonlinear oscillators, each represented by a two-dimensional discrete-time model of the …

The Chialvo hyperneuron model is introduced as the extension of the scalar Chialvo neuron
model in this paper. The complexity of the model is increased not by adding another spatial …

The study of chimera states or, more generally, coherence–incoherence patterns has led to
the development of several tools for their identification and characterization. In this work, we …

Previous results show that some oscillators possess finite number of Wada basins. Here we
find that a nonlinear oscillator can possess a countable infinity of Wada basins and these …

Global resonance is a mechanism by which a homoclinic tangency of a smooth map can
have infinitely many asymptotically stable, single-round periodic solutions. To understand …

The attractors of a dynamical system govern its typical long-term behaviour. The presence of
many attractors is significant as it means the behaviour is heavily dependent on the initial …

The attractors of a dynamical system govern its typical long-term behaviour. The presence of
many attractors is significant as it means the behaviour is heavily dependent on the initial …

This thesis provides new results for homoclinic tangencies, defined below, for smooth
dynamical systems. These objects have an important role in the general theory of dynamical …