Related papers: Parameterized shadowing for nonautonomous dynamics
We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…
We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium that is characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients.…
We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and stable manifold of one of them coincides with…
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical…
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
We characterize certain noncommutative domains in terms of noncommutative holomorphic equivalence via a pseudometric that we define in purely algebraic terms. We prove some properties of this pseudometric and provide an application to free…
We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed pointwise conditions at infinity (in space), which can be time- dependent. Moreover, we study the asymptotic behaviour…
In present paper, we establish sufficient conditions for existence and stability of solutions for system of nonlinear implicit fractional differential equations. The main techniques are based on method of successive approximations. Finally,…
Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…
In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
In this paper we are concerned with $L^p$-maximal parabolic regularity for abstract nonautonomous parabolic systems and their quasilinear counterpart in negative Sobolev spaces incorporating mixed boundary conditions. Our results are…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
We investigate the properties of the shadow cast by a black hole (BH) in a non-commutative spacetime surrounded by a plasma medium. BHs in a plasma environment can exhibit complex interactions that profoundly affect their shadow properties.…
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate…
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always…