Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userVariation of the Dependence of the Transient Process Duration on the Initial Conditions in Systems with Discrete Time
63
0
0.0
(
0
)
Added by
Alexander E. Hramov
Publication date
2006
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Dependence of the transient process duration on the initial conditions is considered in one- and two-dimensional systems with discrete time, representing a logistic map and the Eno map, respectively.
rate research
Read More
Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to the next impact, is derived. Periodic points are found and their stability is determined. The grazing manifold is computed and dynamics is approximated in its vicinity. It is shown that on the grazing manifold there are trapping as well as forbidden regions. Finally, basins of attraction are studied.
This article discusses dependence on initial conditions in natural and social sciences with focus on physical science. The main focus is on the newly discovered rough dependence on initial data.
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.
In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the dynamics of immune escape of other parasites, as well as for the dynamics of multi-strain diseases.
External and internal factors may cause a systems parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a time-delayed oscillator whose time delay varies at a small but non-negligible rate. Our research shows that due to this parameter drift, trajectories from a chaotic attractor tip to other states with a certain probability. This causes the appearance of the phenomenon of transient chaos. By using an ensemble approach, we find a gamma distribution of transient lifetimes, unlike in other non-delayed systems where normal distributions have been found to govern the process. Furthermore, we analyze how the parameter change rate influences the tipping probability, and we derive a scaling law relating the parameter value for which the tipping takes place and the lifetime of the transient chaos with the parameter change rate.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
