China
Africa
Explore chapters and articles related to this topic
Stochastic Modeling Strategies for the Simulation of Large (Spatial) Distributed Systems
Published in Gabriel A. Wainer, Pieter J. Mosterman, Discrete-Event Modeling and Simulation, 2018
Alexandre Muzy, David R.C. Hill
In fundamental domains such as physics, stochastic and spatial modeling enables the understanding of phenomena in which determinism does not offer the same precision (e.g., the spreading of spiral waves); [22]. Here, the effects observed can be understood as a generalization of the concept of stochastic resonance in spatially extended systems. In [23], a study is documented of intracellular spreading of calcium-induced calcium release with the stochastic DeYoung–Keizer-model. The system under study presents a state characterized by backfiring. The backfiring occurs because the steadily propagating pulse solution undergoes a heteroclinic bifurcation (in dynamical systems this type of bifurcation is a global bifurcation involving a heteroclinic cycle that is an invariant set in the phase space of a dynamical system. The use of spatial stochastic modeling was also chosen to argue that quantum-gravitational fluctuations in the space-time background give the vacuum nontrivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light in vacuo [24]. In nuclear medicine, we have shown that the precise detection of small tumors with an error less than 10% can currently only be achieved by spatial Monte Carlo simulations [25].
Behaviour of trajectories near a two-cycle heteroclinic network
Published in Dynamical Systems, 2023
Let be hyperbolic equilibria of (2), where for any , , and , , be a set of trajectories from to , where is assumed. A heteroclinic cycle is an invariant set which is a union of equilibria and heteroclinic connections . A heteroclinic network is a connected union of a finite number of heteroclinic cycles.
Two-dimensional heteroclinic connections in the generalized Lotka–Volterra system
Published in Dynamical Systems, 2023
Consider a smooth dynamical system Let be hyperbolic equilibria of (2), and be a set of trajectories from to , where is assumed. A heteroclinic cycle is an invariant set which is a union of equilibria and heteroclinic connections . A heteroclinic network is a connected union of a finite number of heteroclinic cycles.
Effect of noise on residence times of a heteroclinic cycle
Published in Dynamical Systems, 2023
Valerie Jeong, Claire Postlethwaite
If a heteroclinic cycle is asymptotically stable, trajectories near the cycle get closer to the cycle in forward time. The dynamics near an asymptotically stable heteroclinic cycle shows an intermittent pattern: a solution trajectory spends a long time near an equilibrium, followed by a quick transition to another equilibrium. The time spent in the neighbourhood of equilibrium is known as the residence time. In general, necessary and sufficient conditions for the stability of heteroclinic cycles are hard to determine. However, some partial results for certain classes of heteroclinic cycles have been published [9,15,20,21,24–27].