Related papers: Planar S-systems: Permanence
We prove that the super-linearizability of polynomial systems is preserved by all currently known classes of polynomial automorphisms of $\R^n$. We then establish connections between such automorphisms and a sufficient condition for…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
Optimum lifetime of a series (resp. parallel) system with general standby component(s) always depends on allocation strategy of standby component(s) into the system. Here, we discuss three different models of one or more standby compo-…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
Whereas the positive equilibrium of a mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples,…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove non existence of periodic orbits not contained in this given…
We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the existence of such objects is provided by means of a few basic…
Two cycles are {\em adjacent} if they have an edge in common. Suppose that $G$ is a planar graph, for any two adjacent cycles $C_{1}$ and $C_{2}$, we have $|C_{1}| + |C_{2}| \geq 11$, in particular, when $|C_{1}| = 5$, $|C_{2}| \geq 7$. We…
In this paper we prove the continuity of stable subspaces associated to parabolic-hyperbolic boundary value problems, for limiting values of parameters. The analysis is based on the construction performed in a previous paper of Kreiss' type…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…
A feature of current membrane systems is the fact that objects and membranes are persistent. However, this is not true in the real world. In fact, cells and intracellular proteins have a well-defined lifetime. Inspired from these biological…
In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.
We study non-linear phenomena in double barrier heterostructures. Systems in 3D under the effect of an external magnetic field along the current and 1D systems are analyzed. Non-linearities are reflected in the I-V characteristic curve as…