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To make progress in understanding the issue of memory loss and history dependence in evolving complex systems, we consider the mixing rate that specifies how fast the future states become independent of the initial condition. We propose a simple measure for assessing the mixing rate that can be directly applied to experimental data observed in any metric space $X$. For a compact phase space $X subset R^M$, we prove the following statement. If the underlying dynamical system has a unique physical measure and its dynamics is strongly mixing with respect to this measure, then our method provides an upper bound of the mixing rate. We employ our method to analyze memory loss for the system of slowly sheared granular particles with a small inertial number $I$. The shear is induced by the moving walls as well as by the linear motion of the support surface that ensures approximately linear shear throughout the sample. We show that even if $I$ is kept fixed, the rate of memory loss (considered at the time scale given by the inverse shear rate) depends erratically on the shear rate. Our study suggests a presence of bifurcations at which the rate of memory loss increases with the shear rate while it decreases away from these points. We also find that the memory loss is not a smooth process. Its rate is closely related to frequency of the sudden transitions of the force network. The loss of memory, quantified by observing evolution of force networks, is found to be correlated with the loss of correlation of shear stress measured on the system scale. Thus, we have established a direct link between the evolution of force networks and macroscopic properties of the considered system.
We analyze the transport properties of a set of symmetry-breaking extensions %, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and temporal asymmetries result in the loss of periodicity in momentum direction in the phase space dy
Out-of-time-ordered correlators (OTOC) have been extensively used as a major tool for exploring quantum chaos and also recently, there has been a classical analogue. Studies have been limited to closed systems. In this work, we probe an open classica
We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim textit{et al.},
In spatially located, large scale systems, time and space dynamics interact and drives the behaviour. Examples of such systems can be found in many smart city applications and Cyber-Physical Systems. In this paper we present the Signal Spatio-Tempora
We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state $sigma_i(t) in {0,1}$ of a cell $i$ does not only depend on the states in its local neighborhood at time $t-1$, but also on the memory of its own past s