## What is/are Time Evolving?

Time Evolving - For the paradigmatic Henon-Heiles system, we use both theoretical and numerical arguments to show that the escaping dynamics is non-ergodic independently of the existence of KAM tori, since the chaotic saddle, in whose vicinity trajectories are more likely to spend a finite amount of time evolving before escaping forever, is not utterly spread over the energy shell.^{[1]}We propose a process in which internal representations of objects spend a certain amount of time evolving before we become aware of them.

^{[2]}The Network Analysis unraveled that the significance of sustainability within PPPs has grown over time evolving from traditional developed English-speaking countries to developing countries.

^{[3]}It is found that configurational force and polarization have similar evolution laws in both time evolving and space distribution.

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## Exact Time Evolving

We modify the numerically exact time evolving matrix product operator (TEMPO) method, such that it allows the repeated computation of the time evolution of the reduced system density matrix for various sets of control parameters at very low computational cost.^{[1]}In this paper, exact time evolving rules of target range and Doppler are presented for constant acceleration (CA) and coordinated turn (CT) motions in Cartesian coordinates, and two novel pseudo-spectrum based TBD approaches are proposed for effective detection of weak CA and CT targets in range-Doppler plane, respectively.

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## time evolving model

We investigate the time-dependence of slab thermal structure using dynamically consistent, time evolving models.^{[1]}Multi-stage time evolving models are common statistical models for biological systems, especially insect populations.

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## time evolving block

We analyze the non-equilibrium time evolution of the distribution of the total spin in half of the system and compare the predictions of the semi-semiclassical theory with those of a non-Abelian time evolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry.^{[1]}We simulate coherent driven free dissipative Kerr nonlinear systemnumerically using Euler’smethod by solvingHeisenberg equation ofmotion and time evolving block decimation (TEBD) algorithm, and demonstrate how the numerical results are analogous to classical bistability.

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## time evolving network

We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures.^{[1]}Next, we focus on time evolving networks, where existing nodes and links can disappear, and in parallel new nodes and links may be introduced.

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