Stochastic processes adapted by neural networks with application to climate, energy, and finance

Fixed/Preassigned-Time Stochastic Synchronization of Complex-Valued Fuzzy Neural Networks with Time Delay

“…Choosing T p = 1.5, θ 1 = 1.1, and θ 2 = 0.9, inequality ( 5) is also satisfied. Hence, according to Theorem 2, the drive-response systems (20) and (21) realize PAT synchronization at T p = 1.5. The time evaluation of synchronization errors between systems (20) and ( 21) is shown in Figure 4.…”

“…For m = 3, consider the following CVSFCNNs with time delay: 20) is taken as x 1 (θ) = 0.6 − 0.3i, x 2 (θ) = −1.2 + 0.8i, and x 3 (θ) = −0.4 + 0.8i. The MATLAB numerical simulation of system (20) under the above parameters is shown in Figure 1. It is not difficult to find that system (20) has a chaotic attractor.…”

“…where a i , p i , b i , f , α i , β i , σ i , and I i are defined as in system (20). First, consider the FXT synchronization of the drive-response systems (20) and ( 21) under the controllers (4) and (15). Through simple calculation, we can obtain Re(e i )…”

“…It is not difficult to see that when θ 1 + θ 2 = 2, the system achieves synchronization within the predefined time T p = 1.5, which is even smaller than the fixed-time T 4 max = 2.57327. For controller (19), if we choose T p = 1.2, θ 1 = 1.1, and θ 2 = 0.9, then the drive-response systems (20) and (21) realize PAT synchronization at T p = 1.2. Figure 5 shows the time evaluation of synchronization error between systems (20) and (21) under controller (19).…”

“…For controller (19), if we choose T p = 1.2, θ 1 = 1.1, and θ 2 = 0.9, then the drive-response systems (20) and (21) realize PAT synchronization at T p = 1.2. Figure 5 shows the time evaluation of synchronization error between systems (20) and (21) under controller (19). It is not difficult to see from Figure 5 that when θ 1 + θ 2 = 2, the system achieves synchronization within the predefined time T p = 1.2, which is even smaller than the fixed-time T 4 max = 1.43329.…”