In this paper we explore the dynamics of a one-dimensional Keller–Segel type model for chemotaxis incorporating a logistic cell growth term. We demonstrate the capacity of the model to self-organise into multiple cellular aggregations which, according to position in parameter space, either form a stationary pattern or undergo a sustained spatio-temporal sequence of merging (two aggregations coa...

In this paper we consider a modified spatiotemporal ecological system originating from the temporal Holling-Tanner model, by incorporating diffusion terms. The original ODE system is studied for the stability of coexisting homogeneous steady-states. The modified PDE system is investigated in detail with both numerical and analytical approaches. Both the Turing and non-Turing patterns are examin...

We introduce a technique based on algebraic topology for quantifying spatio-temporally chaotic dynamics. The technique is illustrated using the Gray-Scott and the FitzHugh-Nagumo models.

We investigate signatures of chaos and equilibration in the quantum Rabi model, which exhibits a phase transition when ratio atomic level-splitting to bosonic frequency grows infinity. show that out-of-time-order correlator derived from Loschmidt echo signal quickly saturates normal reveals exponential growth superradiant is associated with onset chaos. Furthermore, we effective time-averaged d...

In this paper, simple autonomous chaotic circuits coupled by resistors are investigated. By carrying out computer calculations and circuit experiments, irregular self-switching phenomenon of three spatial patterns characterized by the phase states of quasi-synchronization of chaos can be observed from only four simple chaotic circuits. This is the same phenomenon as chaotic wandering of spatial...