Suppose that self-mappings are such that, and that there exist nonnegative constants,, satisfying (3.32).
Suppose that self-mappings are such that, and that there exist nonnegative constants,, satisfying, such that for all inequality (3.47).
Suppose that self-mappings are such that, and that for some constant for all there exists (3.1).
In the absence of restrictions on which mappings are acceptable, such mappings are relatively easy to come by.
Figure 8 shows an example of an orbit at a limit-cycle attractor without inputs after eight I/O mappings are learned, such that the orbit (not a transient orbit as shown in Fig. 7) itinerates over the targets in the cyclic order 1, 2, 4, 7, and 5 (12475).
Importantly, we employed a task in which stimulus response outcome mappings were deterministic (in contrast to most reversal paradigms where mappings are probabilistic), such that unexpected outcomes triggered a switch in response set rather than new learning, which is also dopamine-dependent.
Also the Uniqueness of such fixed point are proved, as well as we showed these mappings are -continuous on such fixed points.
The mappings are designed in such a way that the Poincaré Bendixson theorem is satisfied and, consequently, the desired basin of attraction is shaped.
These non-uniform color mappings are designed in such a way that the adjacent glyphs in a table graph that have near underlying values will be assigned with the same color.
