The right-hand side of the evolution Eq. (5) is spatially discretized using the finite difference method, optimized for two-dimensional simulations, and the temporal derivative on the left-hand side is approximated by the forward difference scheme, known as the explicit Euler scheme.
Therefore, motivated by the above studies, we will focus on the complex dynamical behaviors of a simple discrete SIS epidemic model approached by the forward Euler scheme.
The models [9, 22 24] obtained by the forward Euler scheme show complex dynamical behaviors, which are different from the continuous models.
For the discrete population models [22 24] approached by the forward Euler scheme, there existed a flip bifurcation, a Hopf bifurcation and chaos dynamical behaviors which are different from the dynamical behaviors in the corresponding continuous-time models.
Our interest in the present paper is a continuation of the investigation in Yang et al. [33], where we study discretization in time by using the forward Euler scheme.
Equation (1.1) can be viewed as a discrete analogue of the following one-dimensional delay differential equation by using the forward Euler scheme x ˙ ( t ) = − μ x ( t ) + γ x ( t − τ ) ( 1 − x 2 ( t − τ ) ), (1.2).
The "pay it forward" scheme, proposed by students at Portland State University and building on a model developed by the Economic Opportunity Institute, has re-energized debate over ways of alleviating the burden of student debt.
It implements the carry and forward scheme.
Recently, Wang et al. in [20] considered pilot-assisted transmission over wireless sensory relay networks and analyzed scaling laws achieved by the amplify-and-forward scheme in the asymptotic regimes of large nodes, large block length, and small signal-to-noise ratio (SNR) values.
This paper tackles the issue by developing a fuzzy logic-based collaborative forward scheme for integrated file transfer in VANET.
