Related papers: Stochastic calculus: application to dynamic bifurc…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
Many experimental paradigms in neuroscience involve driving the nervous system with periodic sensory stimuli. Neural signals recorded using a variety of techniques will then include phase-locked oscillations at the stimulation frequency.…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
Tipping behavior can occur when an equilibrium of a dynamical system loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
The bifurcation diagram of a model nonlinear Langevin equation with delayed feedback is obtained numerically. We observe both direct and oscillatory bifurcations in different ranges of model parameters. Below threshold, the stationary…
Bifurcation theory is a powerful tool for studying how the dynamics of a neural network model depends on its underlying neurophysiological parameters. However, bifurcation theory has been developed mostly for smooth dynamical systems and…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
Traffic flows are studied in terms of their noise of sound, which is an easily accessible experimental quantity. The sound noise data is studied making use of scaling properties of wavelet transforms and Hurst exponents are extracted. The…
We study stochastic bifurcation for a system under multiplicative stable Levy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z_2 symmetry. Non-classical pitchfork singularities also occur in many non-symmetric systems, where…