Some results on connecting orbits for a class of Hamiltonian systems.
Some results on dynamical systems and their generalization
Some results on Poincaré sets
It is known that a set of positive integers is a Poincaré set (also called intersective set, see I. Ruzsa (1982)) if and only if , where and denotes the Hausdorff dimension (see C. Bishop, Y. Peres (2017), Theorem 2.5.5). In this paper we study the set by replacing with . It is surprising that there are some new phenomena to be worthy of studying. We study them and give several examples to explain our results.
Some results on stability of difference systems.
Some results on the calculus of variations on jet spaces
Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence
Some rigorous results connected with the conventional statistical theory of turbulence in both the two- and three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding cascades. Some of the results are developed here in the case of nonsmooth boundaries and a less regular...
Some unresolved issued in non-linear population dynamics.
The Lyapunov exponent is a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions. Estimates of Lyapunov exponents are often used to characterize the qualitative population dynamics of insect time series. The methodology for estimation of the exponent for an observed, noisy, short ecological time series is still under development. Some progress has been made recently in providing measures of error for these exponents. Studies that do not account...
Spaces of ω-limit sets of graph maps
Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.
Spatially-distributed coverage optimization and control with limited-range interactions
This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect...
Spatially-distributed coverage optimization and control with limited-range interactions
This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with...
Spatiotemporal Dynamics in a Spatial Plankton System
In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially...
Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators.
Special directions on contact metric manifolds of negative -sectional curvature
Special issue: Editorial [Chaos Theory and Technology]
Special issue on the problem of synchronization of nonlinear processes in dynamical systems of different nature and the degree of complexity.
Speciation: A case study in symmetric bifurcation theory.
Specific differential equations for generating pulse sequences.
Spectra of finitely generated Boolean flows.
Spectra of Ruelle Transfer Operators for Contact Flows
In this survey article we discuss some recent results concerning strong spectral estimates for Ruelle transfer operators for contact flows on basic sets similar to these of Dolgopyat obtained in the case of Anosov flows with C1 stable and unstable foliations. Some applications of Dolgopyat's results and the more recent ones are also described.
Spectral and mixing properties of actions of amenable groups.