相关论文: Periodic solutions of piecewise affine gene networ…
In this paper we consider piecewise affine differential equations modeling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph…
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulatory networks. In this paper we elaborate on previous work about control problems for this class of models, using also some recent results…
For flows, the singular cycles connecting saddle periodic orbit and saddle equilibrium can poten- tially result in the so-called singular horseshoe, which means the existence of a non-uniformly hyperbolic chaotic invariant set. However, it…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant delay. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant…
We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
The Conley theory has a tool to guarantee the existence of periodic trajectories in isolating neighborhoods of semi-dynamical systems. We prove that the positive trajectories generated by a piecewise-smooth vector field $Z=(X, Y)$ defined…
The biologist Ren\'e Thomas conjectured, twenty years ago, that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition for this system to produce sustained oscillations. In this…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the…
Based on the results about the invariant cones appeared in the literature this paper analyses the existence of periodic orbits in three-dimensional continuous piecewise linear homogeneous systems with two zones, and a necessary and…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
We consider time-invariant nonlinear $n$-dimensional strongly $2$-cooperative systems, that is, systems that map the set of vectors with up to weak sign variation to its interior. Strongly $2$-cooperative systems enjoy a strong…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…
We consider a cubic nonlinear wave equation on a network and show that inspecting the normal modes of the graph, we can immediately identify which ones extend into nonlinear periodic orbits. Two main classes of nonlinear periodic orbits…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…