The process of pursuit and escape underlies many biological phenomena ranging from predator-prey interactions, combat and sporting activities. Time delays, τ, arise as a consequence of the time taken to identify the opponent, formulate a strategy, and then act upon it. Here we consider virtual stick balancing (VSB) as a delayed pursuit-escape task. The movements of the target in VSB are programmed to resemble those of balancing a stick at the fingertip. A model of delayed pursuit-escape is developed by assuming that the target movements are governed by a simple random walk and the movements of the pursuer by a delayed random walk biased towards the target when τ=0. When τ > 0 the movements can become transiently biased away from the target. The model reproduces the oscillatory dynamics and statistical properties of VSB. For both model and VSB, transients occur in which the pursuer moves inappropriately causing increases in tracking error. The presence of a signature, or trigger, for impending escape suggests the possibility that escapes can be predicted before they occur.
We examine two properties of complex networks, the robustness against targeted node removal (attack) and the transport efficiency in terms of degree correlation in node connection by numerical evaluation of exact analytic expressions. We find that, while the assortative correlation enhances the structural robustness against attack, the disassortative correlation significantly improves the transport efficiency of the network under consideration. This finding might shed light on the reason why some networks in the real world prefer assortative correlation and others prefer disassortative one.
A complex network consisting of nodes and links evolves through time by destroying old links and creating new links. Existing nodes can also be destroyed and new nodes can be created. We introduce a framework based on the evolution of the minimal cycle topology whereby the changes in the network can be characterized through properties of a new similarity network. We demonstrate the methodology by focussing on the local mesoscopic cycle evolution within structural contact networks of quasistatically deforming dense granular materials. At each stage of a prescribed loading program (e.g. biaxial compression subject to constant confining pressure boundary conditions) the assembly of granular particles is represented by a contact network. This complex network is rich in cycle topologies and for each particle we compare the changes to its local mesoscopic cycle topology across a specified strain (or temporal) interval. A similarity network constructed using close topological distance of cycle changes between particles summarizes the structural evolution. Properties of the similarity network including centrality measures and motif structures helps to reveal deformation associated with stick-slip behaviour.
Change-point detection based on an observed time series has emerged as an important method for detecting changes in dynamics of real-world systems. Recently, recurrence networks have been shown to be useful, which are network representations of recurrences, to analyze underlying dynamics. In this paper, we propose a new method for detecting dynamical changes using recurrence networks. The proposed method extracts a group of time indices that share the same dynamics as a community of the recurrence network. In addition, some numerical simulations are presented to verify the validity of this method.
We generally analyze data measured at equal time intervals using fast Fourier transforms (FFTs). However, when for some reason we can only obtain unequally spaced measurement points, then the data become non-uniform and cannot be analyzed directly using FFTs. In this paper, the non-uniform trapezoidal integral discrete Fourier transform (TINUDFT) is proposed to replace the FFT, and is implemented in non-harmonic analysis (NHA) to develop non-uniform NHA (NUNHA) for non-uniform data. NUNHA improved the SNR by over 70 dB compared with the simple non-uniform sinusoidal signal frequency. NUNHA's effectiveness for swept source optical coherence tomography (SS-OCT) is shown by simulation.