Revised perspectives on chaotic and non-chaotic systems By revealing coexisting chaotic and non-chaotic attractors within Lorenz models, Shen and his colleagues proposed a revised view that "weather possesses chaos and order", in contrast to the conventional view of "weather is chaotic". As a result, sensitive dependence on initial conditions (SDIC) does not always appear. Namely, SDIC appears when two orbits (i.e., solutions) become the chaotic attractor; it does not appear when two orbits move toward the same point attractor. The above animation for double pendulum motion provides an analogy. For large angles of swing the motion of the pendulum is often chaotic. By comparison, for small angles of swing, motions are non-chaotic. Multistability is defined when a system (e.g., the double pendulum system) contains more than one bounded attractor that depends only on initial conditions. The multistability was illustrated using kayaking in Figure on the right side (i.e., Figure 1 of 50px Text was copied from this source, which is available under a Creative Commons Attribution 4.0 International License.) where the appearance of strong currents and a stagnant area suggests instability and local stability, respectively. As a result, when two kayaks move along strong currents, their paths display SDIC. On the other hand, when two kayaks move into a stagnant area, they become trapped, showing no typical SDIC (although a chaotic transient may occur). Such features of SDIC or no SDIC suggest two types of solutions and illustrate the nature of multistability.
Revised perspectives on chaotic and non-chaotic systems By revealing coexisting chaotic and non-chaotic attractors within Lorenz models, Shen and his colleagues proposed a revised view that "weather possesses chaos and order", in contrast to the conventional view of "weather is chaotic". As a result, sensitive dependence on initial conditions (SDIC) does not always appear. Namely, SDIC appears when two orbits (i.e., solutions) become the chaotic attractor; it does not appear when two orbits move toward the same point attractor The above animation for double pendulum motion provides an analogy. For large angles of swing the motion of the pendulum is often chaotic. By comparison, for small angles of swing, motions are non-chaotic. Multistability is defined when a system (e.g., the double pendulum system) contains more than one bounded attractor that depends only on initial conditions. The multistability was illustrated using kayaking in Figure on the right side (i.e., Figure 1 of 50px Text was copied from this source, which is available under a Creative Commons Attribution 4.0 International License.) where the appearance of strong currents and a stagnant area suggests instability and local stability, respectively. As a result, when two kayaks move along strong currents, their paths display SDIC. On the other hand, when two kayaks move into a stagnant area they become trapped, showing no typical SDIC (although a chaotic transient may occur). Such features of SDIC or no SDIC suggest two types of solutions and illustrate the nature of multistability.