Related papers: Planar S-systems: Permanence

We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…

This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…

In planar (baby) Skyrme systems, there may be extended linear structures which resemble either domain walls or chains of skyrmions, depending on the choice of potential and boundary conditions. We show that systems with a single vacuum, for…

We consider the Li\'enard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.

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…

We prove Holder continuity for solutions to the n-dimensional H-System assuming logarithmic higher integrability of the solution.

Developing a system of parallel non-linear iterations, we establish the consistency of $\mathfrak{b}<\mathfrak{s}<\mathfrak{d}<\mathfrak{c}$ where $\mathfrak{b}, \mathfrak{d}, \mathfrak{c}$ are arbitrary subject to the known ZFC…

The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern.…

Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…

This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…

This paper proposes a new methodology for design of a stabilizing control law for multi-input linear systems with time-varying, singular gains on the control. The results presented here assume the control gain to satisfy persistence of…

Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems…

Necessary condition to have Hamiltonian cycle in planar graph is given. Examples of regular planar graphs degree three without Hamiltonian cycle are built.

In the paper we define and characterize the asynchronous systems from the point of view of their autonomy, determinism, order, non-anticipation, time invariance, symmetry, stability and other important properties. The study is inspired by…

In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may…

This paper presents new results on the limit cycles of a Li\'enard system with symmetry allowing for discontinuity. Our results generalize and improve the results in [33,34]. The results in [34] are only valid for the smooth system. We…

We study limit cycles in piecewise complex systems with switching manifold $\mathbb{S}^1$. Using M\"obius transformations we establish an equivalence between circular and straight-line discontinuities that preserves periods, stability, and…

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…