Dynamical phases and phase transition in simplicially coupled logistic maps.

Coupled map lattices are a popular and computationally simpler model of pattern formation in nonlinear systems. In this work, we investigate three-site interactions with linear multiplicative coupling in one-dimensional coupled logistic maps that cannot be decomposed into pairwise interactions. We observe the transition to synchronization and the transition to long-range order in space. We coarse-grain the phase space in regions and denote them by spin values. We use two quantifiers the flip rate F (t) that quantify departure from expected band-periodicity as an order parameter. We also study a non-Markovian quantity, known as persistence P (t) to study dynamic phase transitions. Following transitions are observed. (a) Transition to two band attractor state: At this transition F (t) as well as P (t) shows a power-law decay in the range of coupling parameters. Here all sites reach one of the bands. The F (t) as well as P (t) decays as power-law with the decay exponent δ 1 = 0. 4 6 and η 1 = 0. 2 8 , respectively. (b) The transition from a fluctuating chaotic state to a homogeneous synchronized fixed point: Here both the quantifiers F (t) and P (t) show power-law decay with decay exponent δ 2 = 1 and η 2 = 0. 1 1 , respectively. We compare the transitions with the case, where pairwise interactions are also present. The spatiotemporal evolution is analyzed as the coupling parameter is varied. [ABSTRACT FROM AUTHOR]