Our project aims at testing various measures of chaos in time series data from an electrocardiogram (EKG). We examine data from three types of patients who we assume to produce varying EKG dynamics. We use time-delay embedding and calculate correlation dimensions to determine if the data is chaotic or random. Our results indicate that there is some evidence of deterministic chaotic behavior in ...

This paper considers a class of switched dynamical systems to which two periodic inputs are applicable. We derive a one-dimensional (1-D) return map and its derivative analytically for arbitrary shapes of the inputs. Based on the derivative, we introduce a slope chart that displays the relationship between the slope of the return map and that of the inputs. Applying the slope chart to a simplif...

We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor sufficient for the occurrence of chaos. To this purpose, we introduce a class of chaotic two-dimensional systems with Gaussian curvature everywhere positive and...

This paper provides insights about the behavior of chaotic complex systems, and the sensitive dependence of the system on the initial starting conditions. How much does a small change in the initial conditions of a complex system affect it in the long term? Do complex systems exhibit what is called the "Butterfly Effect"? This paper uses an agent-based modeling approach to address these questio...

The problem of chaos suppression by parametric perturbations is considered. Despite the widespread opinion that chaotic behavior may be stabilized by perturbations of any system parameter, we construct a counterexample showing that this is not necessarily the case. In general, chaos suppression means that parametric perturbations should be applied within a set of parameters at which the system ...

We study the behavior of reacting tracers in a chaotic flow. In particular, we look at an autocatalytic reaction and at a bistable system which are subjected to stirring by a chaotic flow. The impact of the chaotic advection is described by a one-dimensional phenomenological model. We use a nonperturbative technique to describe the behavior near a saddle node bifurcation. We also find an approx...

This letter displays, via the numerical simulation of a real digital filter, that a finitestate machine may behave in a near-chaotic way even when its corresponding infinitestate machine does not exhibit chaotic behavior.

Yellow Saddle Goatfish Algorithm (YSGA) is an optimization model inspired by the hunting behavior of yellow saddle goatfish which emulates their collaborative behaviors with chaser fish and blocker fish. To improve global convergence, chaotic maps have been combined YSGA in this paper. Chaotic a nonlinear deterministic system that displays complex, noisy-like, unpredictable behavior. Due to its...

Chaotic behavior arising from very simple non-linear dynamical equation of logistic map makes it was used often in designing chaotic image encryption schemes. However, some properties of chaotic maps can also facilitate cryptanalysis especially when they are implemented in digital domain. Utilizing stable distribution of the chaotic states generated by iterating the logistic map, this paper pre...