We present a chaotic frequency-modulated microwave source that is governed by a simple, first-order nonlinear delay differential equation. When a sinusoidal nonlinearity is incorporated, the dynamical behaviors range from fixed-point to periodic to chaotic, depending on the feedback strength. When the sinusoidal nonlinearity is replaced by a binary nonlinearity, the system exhibits a complex pe...

The double-scroll attractor that can be produced by a wide class of nonlinear electronic circuits is known to contain periodic orbits of all types under certain operating conditions. We identify the branched manifold that describes the double-scroll attractor under these operating conditions. We then show that Ghrist's universal template is embedded as a subtemplate in the double-scroll templat...

This paper studies synthesis of chaotic oscillators using 2-port VCCSs and capacitors. As a rst step, we design a 4-D hysteresis chaotic oscillator using one linear 2-port VCCS, one hysteresis 2-port VCCS and two capacitors. In the circuit, we have con rmed theoretically that a simple periodic attractor changes into quad screw chaotic attractor as in uence of the nonlinearity decreases.

We consider a generalized nonlocal Ginzburg–Landau equation with periodic boundary conditions. For the corresponding initial-boundary value problem we prove existence of solution for all positive values evolution variable. study and properties invariant manifolds. extract class manifolds union which forms global attractor. describe structure attractor find Euclidean dimension its components. In...

This paper presents a simple nonautonomous circuit with a periodic pulse-train input. If the input does not exist, the circuit exhibits either equilibrium attractor or hard oscillation. If a periodic pulse-train input is applied, the circuit exhibits interesting chaotic and periodic attractors. The circuit behavior can be analyzed by a mapping procedure based on a 1-D return map focusing on the...

In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcat...

In this paper, a chaotic switched arrival system is considered. Poincaré section and Poincaré mapping are introduced for defining periodic orbits of this hybrid system. We propose a time-delayed impulsive feedback method to detect unstable periodic orbits embedded in the chaotic attractor. The convergence of the proposed algorithm is proved.

The behavior of a dissipative chaotic dynamical system is determined by the skeleton of its strange attractor, which consists of an uncountably infinite set of unstable periodic orbits. Each orbit is a topological knot, and the set is an infinite link. The types of knots and links supported by the system may be determined by collapsing the attractor along its local stable manifolds to form a te...

A method for multiple access using the structure of the unstable periodic orbits of chaotic attractor is proposed. Possible principles of the control and selection of unstable cycle-codes are presented.

If we allow non-smooth or discontinuous functions in definition of an evolution operator for dynamical systems, then situations of quasi-hyperbolic chaotic dynamics often occur like, for example, on attractors in model Lozi map and in Belykh map. The present article deals with the quasihyperbolic attractor of Belykh in a map describing a rotator with dissipation driven by periodic kicks, the in...