Nature is full of nonlinearities, responsible for a great variety of responses in natural systems. Physiological rhythms constitute a central characteristic of life, which is motivating the analysis of dynamical aspects related to natural systems. Natural rhythms could be either periodic or irregular over time and space and, each kind of dynamical behavior may be related to both normal and pathological physiological functioning. This review article presents an overview of nonlinear dynamics and chaos concepts useful for the analysis of biomedical system. After that, it is presented an overview of dynamical aspects related to different biomedical systems. Cardiovascular rhythms, brain rhythms, cellular and molecular rhythms are discussed from a dynamical approach pointing some characteristics of normal and pathological responses.

This contribution discusses the transient chaos on a pin-ended elasto-plastic beam with both kinematic and isotropic hardening. An iterative numerical procedure, based on the operator split technique, is developed. Numerical simulations show that transient chaos causes sensitivity on initial conditions, which imply that the system response may become unpredictable.

The non-linear dynamics of a pin-ended elasto-plastic beam is discussed in this contribution. Ideal plasticity is in focus. Free and forced responses are considered. An iterative numerical procedure, based on the operator split technique, is developed. This work shows that jump phenomenon and sensitivity to initial conditions imply that the system response may become unpredictable even when a periodic response is expected. Chaotic motion is also associated with the unpredictability of the beam response.

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.