This special issue places its emphasis on the study of the applications of dynamical system
on time scales; such applications include economics models utilizing optimal control theory, fractional calculus, and the development of new population models.
The discrete time dynamical systems
are described by a set of coupled first-order autonomous difference equations [14, 23, 24].
Lastly, that gives a more stronger form of chaos in that the existence of sensitive dependence alone in itself would not and cannot guarantee chaos in dynamical systems
. Hence other routes become relevant in the definition of the types of chaos.
Kuznetsov, "Hidden attractors in dynamical systems
. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and KALman problems to hidden chaotic attractor in Chua circuits," International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol.
Ramm, "Dynamical systems
method for solving operator equations," Communications in Nonlinear Science and Numerical Simulation, vol.
This means that Sharkovsky's Theorem for discrete dynamical systems
associated with continuous functions is not true in the context of PDS.
It is, however, not trivial that the quantities [N.sub.m] have an interpretation in terms of dynamical systems
, as in the case of Artin-Mazur zeta function.
In this Section we put together some notions and facts from the theory of dynamical systems
(both with continuous and discrete time) that are used in our paper.
Mirzakhani found that in dynamical systems
evolving in ways that twist and stretch their shape, the systems' trajectories "are tightly constrained to follow algebraic laws," said McMullen.
Xue, "The global analysis of higher order nonlinear dynamical systems
and the application of cell-to-cell mapping method" Applied Mathematics and Mechanics, vol.
The third section focuses on linear topological conjugacy LTC  and presents equivalent dynamical systems
. In other words the question if the mathematical model under inspection forms an entire class of the dynamical systems
will be answered using similar approach as demonstrated in .
Complex dynamical systems
are considered to be mathematically deterministic because if the initial measurements were certain, it would be possible to derive the end point of their trajectories.