12 research outputs found
Bifurcation Phenomena in Two-Dimensional Piecewise Smooth Discontinuous Maps
In recent years the theory of border collision bifurcations has been
developed for piecewise smooth maps that are continuous across the border, and
has been successfully applied to explain nonsmooth bifurcation phenomena in
physical systems. However, many switching dynamical systems have been found to
yield two-dimensional piecewise smooth maps that are discontinuous across the
border. The theory for understanding the bifurcation phenomena in such systems
is not available yet. In this paper we present the first approach to the
problem of analysing and classifying the bifurcation phenomena in
two-dimensional discontinuous maps, based on a piecewise linear approximation
in the neighborhood of the border. We explain the bifurcations occurring in the
static VAR compensator used in electrical power systems, using the theory
developed in this paper. This theory may be applied similarly to other systems
that yield two-dimensional discontinuous maps
Existence of chaos in a piecewise smooth two-dimensional contractive map
Piecewise smooth maps occur in a variety of physical systems. We show that in a two-dimensional continuous map a chaotic orbit can exist even when the map is contractive (eigenvalues less than unity in magnitude) at every point in the phase space. In this letter we explain this peculiar feature of piecewise smooth continuous maps
Augmentation of dynamical persistence in networks through asymmetric interaction
There exists several natural instances in which systems may undergo through local degradation of its constituting elements. This may severely affect the overall dynamical activity in unexpected ways. So, it requires to overcome such situations while posing some appropriate mechanisms. In this work we investigate aging networks comprising different groups of dynamical units coupled locally, non-locally or globally. We provide a mechanism that deals with asymmetry in the interaction of active and inactive groups to enhance the dynamical robustness of such aging networks. Apart from numerical experiments, we provide analytical treatment to identify the critical phase transition. Mathematical results are found to perfectly match the outcomes obtained through numerical experiments. Moreover, we provide evidence of the enriched network survivability in more complex topologies considering small-world and scale-free networks. Our proposed method to enhance the dynamical robustness is thus independent of coupling topology and quite efficient in aging networks of coupled oscillators
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Time delays shape the eco-evolutionary dynamics of cooperation.
We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoners dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems
Time delays shape the eco-evolutionary dynamics of cooperation
We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner’s dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems