Chaos and geometric order in architecture and design.
Chaos and shadowing around a homoclinic tube.
Chaos: Challenges from and to socio-spatial form and policy.
Chaos control and hybrid projective synchronization of a novel chaotic system.
Chaos control of a fractional-order financial system.
Chaos in a predator-prey system with impulsive perturbations and stage structure for the predator.
Chaos in ecology: The topological entropy of a tritrophic food chain model.
Chaos in nonautonomous dynamical systems.
Chaos in some planar nonautonomous polynomial differential equation
We show that under some assumptions on the function f the system generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.
Chaos made visual.
In this paper we show how the main properties of chaos can be fully visualized at the light of a very easy to handle object, the tent function. Although very concrete, this case is representative of a very large number of examples, with more or less the same properties.
Chaos synchronization between two different fractional systems of Lorenz family.
Chaos synchronization of a fractional nonautonomous system
In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the effectiveness of the proposed methods.
Chaotic attractor generation via a simple linear time-varying system.
Chaotic attractors of two-dimensional invertible maps.
Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium
By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived...
Chaotic behavior of the biharmonic dynamics system.
Chaotic behaviour in the solar system
Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model
We focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion , where are continuous and at every point . It seems this chaotic behaviour is typical for such dynamical system. In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called the IS-LM model....
Chaotic behaviour of the map x ↦ ω(x, f)
Let K(2ℕ) be the class of compact subsets of the Cantor space 2ℕ, furnished with the Hausdorff metric. Let f ∈ C(2ℕ). We study the map ω f: 2ℕ → K(2ℕ) defined as ω f (x) = ω(x, f), the ω-limit set of x under f. Unlike the case of n-dimensional manifolds, n ≥ 1, we show that ω f is continuous for the generic self-map f of the Cantor space, even though the set of functions for which ω f is everywhere discontinuous on a subsystem is dense in C(2ℕ). The relationships between the continuity of ω f and...
Chaotic dynamics and nonlinear feedback control