Related papers: Invariant critical sets of conserved quantities
Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This letter shows that a class of such systems have amazing features of (1) supersensitivity…
We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a…
We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and…
Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…
Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of…
Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com putations update internal states and…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…
Systems whose variable are constrained to be positive allow computationally efficient control design. We generalize these results to linear systems which leave a cone invariant. This is a wider class of systems than positive systems. We…
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…