In this study, we used recurrence quantification analysis (RQA) and recurrence plots (RPs) to compare the movement activity of individual workers of three ant species, as well as a gregarious beetle species. RQA and RPs quantify the number and duration of recurrences of a dynamical system, including a detailed quantification of signals that could be stochastic, deterministic, or both. First, we...

Recurrence-plot–based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantific...

Stability investigation of hereditary systems is connected often with construction of Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed in [1-9] both for differential equations with aftereffect and for difference equations with discrete time. Here, some modification of Lyapunov-type stability theorem is proposed, which allows one to use thi...

The nonlinear difference equation (E) xn+1 − xn = anφn(xσ(n)) + bn, where (an), (bn) are real sequences, φn : −→ , (σ(n)) is a sequence of integers and lim n−→∞ σ(n) =∞, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation yn+1 − yn = bn are given. Sufficient conditions under which for every real consta...

Following the method of combinatorial telescoping for alternating sums given by Chen, Hou and Mu, we present a combinatorial telescoping approach to partition identities on sums of positive terms. By giving a classification of the combinatorial objects corresponding to a sum of positive terms, we establish bijections that lead a telescoping relation. We illustrate this idea by giving a combinat...

Research Problem Formulation. Modern financial markets are characterized by considerable complexity of the processes occurring in them. There is a globalization of international markets; currency, interest rate, rate of securities, staple prices volatility are increasing, and as a result, financial markets have become more volatile, complex and risky. An instrument of monitoring system of a sto...

This paper presents a new method of evaluating heart rate variability based on nonlinear analysis. We can describe selected processes generated in living organism much more effectively using specific methods of nonlinear analysis. The main tool of recurrence analysis is represented by recurrence plots which visualise the recurrence behaviour of the phase space trajectory of dynamical systems.

Environmental systems and time series emanating from such systems present a particular interest. System state transitions can occur in time and/or in space and the detection of such transitions can be particularly useful in the design related to such systems. Since the majority of physical systems present non linear behavior the use of appropriate tools is necessary. Recurrence Plots (RPs) and ...

Given a set of time series, our goal is to identify prototypes that cover the maximum possible amount of occurring subsequences regardless of their order. This scenario appears in the context of the automotive industry, where the goal is to determine operational profiles that comprise frequently recurring driving behavior patterns. This problem can be solved by clustering, however, standard dis...