Stable manifoldIn mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set. The gravitational tidal forces acting on the rings of Saturn provide an easy-to-visualize physical example. The tidal forces flatten the ring into the equatorial plane, even as they stretch it out in the radial direction.
Chaos theoryChaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.
Cardiac cycleThe cardiac cycle is the performance of the human heart from the beginning of one heartbeat to the beginning of the next. It consists of two periods: one during which the heart muscle relaxes and refills with blood, called diastole, following a period of robust contraction and pumping of blood, called systole. After emptying, the heart relaxes and expands to receive another influx of blood returning from the lungs and other systems of the body, before again contracting to pump blood to the lungs and those systems.
Hénon mapIn mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point (xn, yn) in the plane and maps it to a new point The map depends on two parameters, a and b, which for the classical Hénon map have values of a = 1.4 and b = 0.3. For the classical values the Hénon map is chaotic. For other values of a and b the map may be chaotic, intermittent, or converge to a periodic orbit.
PulseIn medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the neck (carotid artery), wrist (radial artery), at the groin (femoral artery), behind the knee (popliteal artery), near the ankle joint (posterior tibial artery), and on foot (dorsalis pedis artery). Pulse (or the count of arterial pulse per minute) is equivalent to measuring the heart rate.
Ventricular fibrillationVentricular fibrillation (V-fib or VF) is an abnormal heart rhythm in which the ventricles of the heart quiver. It is due to disorganized electrical activity. Ventricular fibrillation results in cardiac arrest with loss of consciousness and no pulse. This is followed by sudden cardiac death in the absence of treatment. Ventricular fibrillation is initially found in about 10% of people with cardiac arrest. Ventricular fibrillation can occur due to coronary heart disease, valvular heart disease, cardiomyopathy, Brugada syndrome, long QT syndrome, electric shock, or intracranial hemorrhage.
Butterfly effectIn chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier.
Human embryonic developmentHuman embryonic development, or human embryogenesis, is the development and formation of the human embryo. It is characterised by the processes of cell division and cellular differentiation of the embryo that occurs during the early stages of development. In biological terms, the development of the human body entails growth from a one-celled zygote to an adult human being. Fertilization occurs when the sperm cell successfully enters and fuses with an egg cell (ovum).
AMPA receptorThe α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (also known as AMPA receptor, AMPAR, or quisqualate receptor) is an ionotropic transmembrane receptor for glutamate (iGluR) that mediates fast synaptic transmission in the central nervous system (CNS). It has been traditionally classified as a non-NMDA-type receptor, along with the kainate receptor. Its name is derived from its ability to be activated by the artificial glutamate analog AMPA.
Cauchy boundary conditionIn mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.
