We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron–Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...

The Bird and Nanbu systems are particle systems used to approximate the solution of Boltzmann mollified equation. In particular, they have the propagation of chaos property. Following [GM94], we use coupling techniques and results on branching processes to write an expansion of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems than the ...

Three different types of chaotic behavior and instabilities (homoclinic chaos, hyperbolic resonance, and parabolic resonance) in Hamiltonian perturbations of the nonlinear Schrödinger (NLS) equation are described. The analysis is performed on a truncated model using a novel framework in which a hierarchy of bifurcations is constructed. It is demonstrated numerically that the forced NLS equation...

Data hiding is also known as data encapsulation or information hiding, it reduces system complexity for increased robustness .Proposed approach provides optimal solution for performing data hiding. The goal of data hiding technique is to embed the secret data into the cover image with minimum changes in the pixel values. Here the secret data is generated and embedded into the cover image by ran...

Doubling of torus occurs in high dimensional nonlinear systems, which is related to a certain kind of typical second bifurcations. It is a nontrivial task to create a torus-doubling solution with desired dynamical properties based on the classical bifurcation theories. In this paper, dead-beat hybrid projective synchronization is employed to build a novel method for designing stable torus-doubl...

The Bird and Nanbu systems are particle systems used to approximate the solution of Boltzmann mollified equation. In particular, they have the propagation of chaos property. Following [GM94], we use coupling techniques and results on branching processes to write an expansion of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems than the ...

In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurc...

Aiming to the demand and characteristics of vehicle scheduling optimization problem in emergency rescue, this paper establishes a multi-objective optimization model, which takes minimizing variable bidirectional distance, path risk and cost as the optimization target. To avoid the prematurely falling into local optimization of ant colony system(ACS)algorithm, and to improve the algorithm adapta...

We investigate bifurcation and chaos observed in coupled BVP neurons with external impulsive forces. Although the single neuron without the external force has only one equilibrium point, combining these n (n ≥ 3) neurons unidirectionally in a ring, nphase periodic solutions are generated. Applying the impulsive forces, successive period-doubling bifurcations of the n-phase solution occur and ch...

An application of recent uncertainty quantification techniques to Wind Engineering is presented. In particular, the study of the effects of small geometric changes in the Sunshine Skyway Bridge deck on its aerodynamic behavior is addressed. This results in the numerical solution of a proper PDE posed in a domain affected by randomness, which is handled through a mapping approach. A non-intrusiv...