Related papers: Instability and bifurcation in a trend depending p…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
Bouncing solutions are obtained from a generally covariant action characterized by a potential which is a nonlocal functional of the dilaton field at two separated space-time points. Gradient instabilities are shown to arise in this context…
We have found an oscillating instability of fast-running cracks in thin rubber sheets. A well-defined transition from straight to oscillating cracks occurs as the amount of biaxial strain increases. Measurements of the amplitude and…
Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
A Hopf bifurcation theorem is established for the abstract evolution equation $\frac{\mathrm{d}x}{\mathrm{d}t}=F(x,\lambda)$ in infinite dimensions under the degeneracy condition $Re \mu ^{\prime}(\lambda_0)= 0$ and suitable assumptions.…
We review the evidence that the erratic dynamics of markets is to a large extent of endogenous origin, i.e. determined by the trading activity itself and not due to the rational processing of exogenous news. In order to understand why and…
We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
It has long been recognized that the key to understand kinetic friction force $F_k$ is the analysis of microscopic instabilities that lead to sudden irreversible "pops" of certain degrees of freedom. In this Letter, the nature of such…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…
We give an account of the various changes in the stability character in the five types of Riemann ellipsoids by establishing the occurrence of different quasi-periodic Hamiltonian bifurcations. Suitable symplectic changes of coordinates,…
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables…
We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary,…
We report on a novel behavior of solitary localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to nontrivial…
We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription.…