Chaos and control of discrete dynamic traffic model

Polynomial Approach and Non-linear Analysis for a Traffic Fundamental Diagram

“…As it is already known for similar iterative schemes [6,7,12], this cyclic behaviour doubles its period in a manner described by the mapping in Figure 13. Velocity v is a parameter that triggers such behaviour as established now.…”

“…Some of them are made from continuous functions [6,13] and others are constructed in a piecewise manner [3]. All of them try to include the variables and parameters that are involved in the traffic phenomena in order to achieve a better fitness of the corresponding data that validate those models.…”

“…This function is chosen because of the non-symmetric form observed in real density-flow diagram, instead of a quadratic form that would necessarily suppose a symmetric parabola [6]. …”

“…This proposal has arisen because a similar approach has been attempted with the well-known logistic equation, taken as a valid traffic relation [6] but missing some specifications that a fundamental diagram does have, resulting in an interesting but incomplete analysis [12].…”

Adaptive synchronization for nonlinear FitzHugh–Nagumo neurons in external electrical stimulation

“…synchronization can be applied in the wide fields of physics and engineering systems such as power converters, chemical reactions, biological systems, information processing, and especially for secure communication [9][10][11][12][13]. Many different control strategies have been developed for chaotic systems such as impulsive control [14,15], adaptive control [16,17], sliding mode control [18,19], feedback control [20], optimal control [21], digital redesign control [22], backstepping control [23,24], and so on.…”