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AbstractWe present techniques for classifying Markov chains with a continuous state space as either ergodic or recurrent. These methods are analogous to those of Foster for countable space chains. The theory is presented in the first half of the paper, while the second half consists of examples illustrating these techniques. The technique for proving ergodicity involves, in practice, three steps: showing that the chain is irreducible in a suitable sense; verifying that the mean hitting times on certain (usually bounded) sets are bounded, by using a "mean drift" criterion analogous to that of Foster; and finally, checking that the chain is such that bounded mean hitting times for these sets does actually imply ergodicity.The examples comprise a number of known and new results: using our techniques we investigate random walks, queues with waiting‐time‐dependent service times, dams with general and random‐release rules, the s‐S inventory model, and feedback models.

Understanding the underlying processes and extracting detailed characteristics of rivers is critical and has not yet been fully developed. The purpose of this study was to examine the performance of non-linear time series methods on environmental data. Specifically, we performed an analysis of water level measurements, extracted from sensors, located on specified stations along the Nestos River (Greece), with Recurrence Plots (RP) and Recurrence Quantification Analysis (RQA) methods. A more detailed inspection with the sliding windows (epoqs) method was applied on the Recurrence Rate, Average Diagonal Line and Trapping Time parameters, with results showing phase transitions providing useful information about the dynamics of the system. The suggested method seems to be promising for the detection of the dynamical transitions that can characterize distinct time windows of the time series and reveals information about the changes in state within the whole time series. The results will be useful for designing the energy policy investments of producers and also will be helpful for dam management assessment as well as government energy policy.

Dynamics of arable and pastoral farming systems in Scotland over the period 1867–2020 are documented using time series analysis methods, including for nonlinear dynamical systems. Results show arable and pastoral farming, at a national scale, are dynamic over a range of timescales, with medium- and short-term dynamics associated with endogenous system forces and exogenous factors, respectively. Medium-term dynamics provide evidence of endogenous systems-level feedbacks between farming sectors responding to change in world and national cereal prices as an economic driver, and act to dampen impacts of exogenous shocks and events (weather, disease). Regime shifts are identified in national cereal prices. Results show change and dynamics as emergent properties of system interactions. Changes in dynamics and strength of endogenous dampening over the duration of the study are associated with dynamical changes from major governmental policy decisions that altered the boundary conditions for interdependencies of arable and pastoral farming.

AbstractThis article examines the recurrence of violence in the contemporary world based on the premise that states can use their monopoly of violence not only for preserving the life of their citizens but also for the sake of terror and annihilation. This ambiguous nature of the use of violence derives from the fact that the legal order of the state is a function of concrete acts of bloodshed and killing. The state bases the law on violence because authorities fear the psychological attraction that bloodshed has on the human imagination. The contagious character of violence, however, is not based on man's innate potential for aggression. Rather, it depends on the nature of the reciprocity of social relations. Violent conflict often feeds on negative social communication such as hatred and desire for vengeance. Yet, faced with the inevitable recurrence of violence humans have the capacity to act on the spiral of vengeance. One possible way to pacify violence is to transform the destructive, negative reciprocity of retaliation into the creative, positive reciprocity of active non‐violence.