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The purpose of this paper is to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map.

At the beginning of the twentieth century, Poincare's recurrence theorem had revolutionized modern mechanics and statistical physics. However, this theorem did not attract considerable attention, at least from a numerical and computational point of view. In a series of relatively recent papers, Balakrishnan, Nicolis and Nicolis have addressed the recurrence time problem in a firm basis, introducing notation, theory, and numerical studies. Motivated by this call, the paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map. The authors propose here in different tests and computations, each one illuminating the many aspects of the problem of recurrence. The paper ends up with a short discussion and conclusions.

In this paper, the authors obtain new results on computations, each one illuminating the many aspects of the problem of recurrence. One striking aspect of this detailed work, is that when the sizes of the cells in the phase space became considerable, then the recurrence times assume ordinary values.

The paper extends previous results on chaotic maps to the logistic map, enhancing comprehension, making possible connections with number theory, combinatorics and cryptography.

This study is a follow-up of inpatients diagnosed with severe depression/melancholia between 1956 and 1969. During this period, all inpatients at the Department of Psychiatry, University Hospital, Lund, were rated on a multidimensional diagnostic schedule on discharge. There were 471 patients born from 1920 onward. In the present follow-up, 2006 to 2010, 169 survivors could be traced. They were asked to participate in the study involving a telephone interview, in which a structured life chart was used. Of the patients contacted, 16 were ill or confused and 3 did not remember ever being depressed, leaving 150 who could participate. Seventy-five of these agreed to participate in the study. Long-term course of depression was evaluated by cluster analysis and compared to background variables, such as heredity for depression, perceived parental rearing behaviour, and treatment of index depressive episode. Using a cluster analysis the patients could be separated into six clusters describing the course: i) single or few episodes followed by long-lasting remission; ii) single or few episodes followed by long-lasting remission, although shorter; iii) single or few episodes followed by late recurrence; iv) single or few episodes, but more frequently ill, followed by late recurrence; v) several episodes followed by lasting remission; vi) chronic course of episodes. Remission or recurrence could therefore occur even after more than a decade. In summary, there was a short-term course with or without recurrence or a chronic course with or without late remission. Heredity for depression was significantly related to a chronic course with or without late remission.

The purpose of this paper is to determine the factors associated with DF occurrence in recurrence villages in Chiang Rai, Thailand.

A case-control study was conducted between June 2017 and December 2017. A validated questionnaire was used to detect the factors associated with recurrence of DF. χ² and logistic regression were used to detect the associations between variables at α=0.05.

In total, 213 cases and 436 controls were recruited into the analysis. Cases were recruited from 20 DF recurring villages, while controls were recruited from 20 non-DF recurring villages in Chiang Rai province. At community level, three variables were associated with recurrence of DF; size of the village (p=0.007), number of villagers (p=0.009), tribe (p=0.043) and distance to a hospital (p=0.003). Three variables were associated with DF at personal and family levels in multivariate model: children whose parents worked as daily employees, and government officers and traders were more likely to have DF 1.56 (95%CI=1.22–2.48) and 4.31 (95%CI=4.66–9.38) times greater than of those whose parents’ worked as agriculturists, respectively; children aged less than one year were 2.89 (95%CI=2.17–4.33) times more likely to have DF than those aged=6 and children who were under standard growth and over standard growth were more likely to have DF than those standard growth 1.61 (95%CI=1.18–2.53) and 7.33 (95%CI=4.39–10.37) times, respectively.

This is the original research article which was conducted in detecting the factors associated with recurrence of DHF in Northern Thailand.

The purpose of this paper is to study the dynamic features of friction coefficient during running-in state based on recurrence analysis, so as to recognize the running-in state of crankshaft journal bearings.

The friction coefficient was measured in the friction experiments and the dynamic features are analyzed by recurrence plots (RPs), unthreshold recurrence plots (URPs) and recurrence quantification analysis.

During the running-in process, RPs have gone through disrupted patterns, drift patterns and homogeneous patterns successively. URP shows that the phase trajectory spirals in the disrupted pattern gradually converge in the drift pattern and remain stable in the homogeneous pattern. Three independent measures, recurrence rate, entropy and laminarity, are chosen to characterize friction coefficient from the perspective of point, diagonal line and vertical line structures of the RPs.

The results provide a feasible way to monitor the running-in process and recognize the running-in state.

AISI 52100-AISI 1045 specimens were used as the ring-on-disc tribopairs in the experiments to investigate the stability of friction process.

The coefficient of friction (COF) signals were measured throughout the friction process and the recurrence plots (RPs) and recurrence quantification analysis (RQA) are adapted to analyze the stability of the tribosystem.

The results show that the COF time-series acquired from different tests possess the same dynamic evolution laws. The evolution of RPs follows the rules of “disrupted-homogeneous-disrupted,” which corresponds to the “running-in, steady-state and increasing stages” of friction process. Additionally, the evolution laws of RQA measures LAM, Vmax and TT accord with the “bathtub curve.” Therefore, both RPs and RQA measures can inform quantitative interpretations of tribological behaviors and friction process identification.

The both RPs and RQA are capable of characterizing the tribological behaviors and can depict the various stages of friction process.

This paper aims to investigate that how to mitigate the weaker party's risk perception in imbalanced supply chain relationships by framing contracts according to complexity and recurrence. The level of information technology (IT) integration is considered as the moderator influencing the effectuation of contract framing.

The authors conducted a questionnaire survey with 229 firms involved in imbalanced supply chains. Hierarchical regression analysis was used to test the hypotheses.

The authors found contractual complexity positively influenced performance and relational risk, while contractual recurrence negatively impacted performance and relational risk. This study further reveals the positive moderating effect of IT integration in influencing contractual complexity on relational risk and performance risk and the negative impact of IT integration in influencing contractual recurrence on relational risk and performance risk.

Overall, this study posits the coordinating role of contracts in reducing the weaker party's risk perception in imbalanced supply chain relationships.

The authors concluded by illustrating how to customize contracts based on the level of IT integration to maximize their role in reducing risk perception.

This study is embedded in imbalanced supply chain relationship, aiming to solve the problem of high-risk perception held by the weaker party, which is a salient threat to the sustainability of collaboration. Contract framing is proposed as an effective approach for mitigating risk perception, which should be carefully designed based on the level of IT integration of the relationship. The authors found that contractual complexity has a positive influence on performance and relational risk, but contractual recurrence has a negative impact on performance and relational risk. This study further reveals the moderating effect of IT integration on the effectuation of contractual framing.

The purpose of this paper is to examine the possibility of biotic patterns. In economics, markets are thought to tend to equilibrium with random and unpredictable deviations. However, an explosion of empirical work searching for possible chaos show an enormous amount of unexplained nonlinear structure. These observations led the authors to examine the possibility of biotic patterns in economics.

Bios is defined as a causally generated creative process. It is the causal counterpart to random walk, just as chaos is the causal equivalent to randomness. Economic data consisting of time series from several categories, including banking, employment and population, and gross domestic product and components, were studied for diversification, recurrence, and predictability patterns characteristic of bios. Diversification was quantified as increased variance with embedding, recurrences were measured using newly developed computer programs, and predictability was measured with a nonlinear prediction method.

Dynamic analyses of the data show: episodic patterning and asymmetric statistical distribution, typical of bios; increase in variance with embedding (diversification), less recurrence than shuffled copies of the data (novelty), demonstrating creativity; consecutive recurrence; and patterning in the series of differences, indicating non‐random causation.

The demonstration of bios in empirical data indicates that the economy is non‐stationary, causal, and creative. This contradicts the notion that markets regulate themselves and tend to equilibrium, and the characterization of market variation as random or chaotic. Further economic crises may be avoided by acknowledging that financial markets are not bound within limits and can be modified into new forms by human action.

The purpose of this research is to investigate the time structure characteristics of collaborative knowledge production behaviors in Q&A (question-and-answer) communities for explicit and tacit knowledge, and systematically investigate the supply side and the demand side of knowledge production.

Taking Zhihu as the research object, using the methods of recurrence plot and recurrence quantification analysis, this paper analyzes the recursive characteristics of the motion trajectories of the three behavioral sequences of questioning, answering, and discussion, qualitatively and quantitatively analyzing the generation and evolution mechanism of explicit and tacit knowledge.

The results show that compared with the demand-side behavior sequence, the supply-side behavior sequence exhibits higher stability, complexity and periodicity. Compared with the tacit knowledge topics, the demand-side behavior sequence of the explicit knowledge topics shows stronger nonlinearity, and the supply-side behavior sequence shows lower complexity.

The research conclusions provide preliminary evidence for the effectiveness of the recurrence plot method in distinguishing different types of knowledge production behaviors and have important application value for the “crowdsourcing” knowledge generation and identification under the knowledge economy and the sustainable development of the socialized question-and-answer community.

It has long been challenged that the distributions of empirical returns do not follow the log-normal distribution upon which many celebrated results of finance are based including the Black–Scholes Option-Pricing model. Borland (2002) succeeds in obtaining alternate closed form solutions for European options based on Tsallis distribution, which allow for statistical feedback as a model of the underlying stock returns. Motivated by this, we simulate two distinct time series based on initial data from NIFTY daily close values, one based on the Gaussian return distribution and the other on non-Gaussian distribution. Using techniques of non-linear dynamics, we examine the underlying dynamic characteristics of both the simulated time series and compare them with the characteristics of actual data. Our findings give a definite edge to the non-Gaussian model over the Gaussian one.

This paper aims to analyze transient and steady state processes in series resistive capacitive-circuits when the supplied voltage is a sequence of periodic rectangular pulses. The purpose is to obtain an analytical formula for the capacitor voltage at any instant of time, both for the transient and the steady-state processes.

The main approach is to use a combination of differential and recurrence equations.

An analytical expression (formula) for obtaining the capacitor voltage at any instant of time has been found.

The results obtained are new. They are much more convenient to use than the results obtained by the Fourier series. The exposed approach can also be used in other circuits and other forms of the supplied voltage.