Abstract. In this paper, the linear feedback controlling of a novel chaotic system is discussed. The chaotic system is a new attractor which is similar to the Lorenz chaotic attractor, but it is not topological equivalent with the Lorenz chaotic system. This Letter proposes a novel approach for controlling this new attractor by linear feedback functions. The results obtained in this paper show ...

A chaotic attractor solution of the Lorenz system [1] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [2] with a similar foliated structure is also established.

In this paper, we consider the long time behavior of solutions for two-dimensional generalized Benjamin-Bona-Mahony equations with periodic boundary conditions. By the method of orthogonal decomposition, we show that the existence of asymptotic attractor from the precision of approximate inertial manifolds. Moreover, the dimensions estimate of the asymptotic attractor is obtained.

Periodically driven two-dimensional nonlinear oscillators can generate strange attractors that are periodic. These attractors are mapped in a locally 1-1 way to entire families of strange attractors that are indexed by a pair of relatively prime integers (n(1),n(2)), with n(1)>/=1. The integers are introduced by imposing periodic boundary conditions on the entire strange attractor rather than i...

We consider a class of differential equations, ẍ + γẋ + g(x) = f(ωt), with ω ∈ R, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasi-periodicity as the forcing. For g(x) = x, p ∈ N, we show that, when the dissipation coefficient is large enough, there is only one such...

In our previous paper, it was confirmed that the unstable periodic orbit embedded in the chaotic attractor in magneto-elastic beam system can be stabilized by delayed feedback control experimentally. It seems an advantage that the control method does not require any exact model of the system. However, the application of the control raises the problem that we cannot predict the stabilized unstab...

One of the key questions about gene regulatory networks is how to predict complex dynamical properties based on influence graph’s topology. Earlier theoretical studies have identified conditions for properties, like multistability or oscillations, topological features, presence a positive (negative) feedback loop. This work follows this path and aims find sufficient necessary condition existenc...

Invariant sets embedded in a chaotic attractor can generate time averages that diier from the average generated by typical orbits on the attractor. Motivated by two diierent topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We presen...

Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I intermittency. The largest nontrivial Lyapunov exponent Λ is a good order–parameter for this route from chaos to SNA to periodic motion: the signature is di...