The motive of this work is to present a computational design using the stochastic scaled conjugate gradient (SCG) neural networks (NNs) called as SCGNNs for the socio-ecological dynamics (SED) with reef ecosystems and conservation estimation. The mathematical descriptions of the SED model are provided that is dependent upon five categories, macroalgae

The study of coral reef ecology systems (CRESs) or complex aquatic networks along with the composed construction based on the Scleractinia corals have located on their reigns skeletons [

The Caribbean form the CRESs demonstrates the elasticity in the contradiction of the past conflicts and recovered quickly after the Hurricane Allen (1980–1983) [

The mathematical form of the systems along with the diverse perceptions have been functional in numerous submissions of the religion, non-physical form of the models (psychology, sociology, political science, economics), linguistics, engineering studies (computer science, mechanical, electrical), philosophy, and in the dynamics of the natural science (earth sciences, biology, chemistry, physics). A mathematical model is applied to scrutinize the influences of numerous apparatuses. The mathematical systems have been provided in several measures, like game theory, statistics, and well as dynamic systems. In general, mathematical systems can indicate the logical strategies, while the scientific measures exhibit the brilliance of the models that indicate the theoretical performances to support the consequences of the repeatable actions. The mathematical form of the systems has been illustrated in the ecosystem management [

The human conducts and the dynamic impacts based on the CRESs require more investigations to model the theoretical form of the systems. Several anthropogenic influences have been used to reproduce the present work based on the reef protection along with the covered areas of marine [

The mathematical form of the socio-ecological dynamics (SED) using the reef ecosystems and the conservation estimation model is provided in five categories, Macroalgae

The starting four dynamics in the

Parameters | Details |
---|---|

Human judgement | |

Algal turf | |

Live coral | |

Macroalgae | |

Density of parrotfish | |

Growth rate of Macroalgal | |

Macroalgal overgrowth corals rate | |

Growth ratio of coral | |

Growth ratio of parrotfish | |

Mortality ratio of coral | |

Standardized yield and the sociologically plausible behaviour | |

Mortality rate of human-induced parrotfish | |

Time | |

Initial conditions |

The motive of the present work is to provide a computational design using the stochastic scaled conjugate gradient (SCG) neural networks (NNs) called as SCGNNs for the SED with reef ecosystems and conservation estimation. The stochastic frameworks have been used to provide the results of several evolutionary/swarming schemes [

A novel design of the SCGNNs is presented to solve the SED with reef ecosystems and conservation estimation using the SCGNNs.

The comparison of the achieved performances via SCGNNs and the database Runge-Kutta solutions has been presented to solve the SED model.

The overlapping of the outcomes designates the accuracy and correctness of the proposed stochastic SCGNNs procedure for solving the mathematical SED nonlinear model.

The precise and accurate absolute error (AE) presentations designate the excellence of the stochastic designed SCGNNs approach to solving the SED mathematical model.

The presentations via correlation values, STs, EHs, MSE measures and regression analysis provide the accurateness of the stochastic designed SCGNNs approach for the nonlinear SED systems.

The remaining sections of the paper are organized as: Section 2 is based on the stochastic methodology. Section 3 provides the numerical procedures of the SED model. Section 4 derives the concluding remarks of the present study.

The proposed methodology based on the SCGNNs is described in two phases for solving the SED with reef ecosystems and conservation estimation. The process of optimization based on the multi-layer procedures is provided in

The designed SCGNNs is implemented using the ‘nftool’ solver in ‘Matlab’ for the appropriate portions of hidden neurons, testing statistics, learning methods and verification statics. While the process of implementation based on the SCGNNs for solving the SED mathematical system based on the parameter setting is provide in

Index | Settings |
---|---|

Fitness goal (MSE) | 0 |

Maximum learning epochs | 300 |

Adaptive parameter (mu) | 0.004 |

Increasing factor for the Mu | 9 |

Decreeing factor for the Mu | 0.09 |

Maximum Mu values | 10^{10} |

Minimum gradient values | 10^{−06} |

Authentication fail count | 7 |

Hidden neurons | 13 |

Testing samples | 11% |

Authorization samples | 12% |

Training samples | 77% |

Sample assortment | Arbitrary |

Output, hidden and Input Layers | Single |

Dataset generation | Runge-Kutta method |

Runge-Kutta terminating and execution procedure | Default |

This section presents the numerical representations using the proposed SCGNNs for three different variations based on the mathematical form of the SED with reef ecosystems and conservation estimation are mathematically given as:

The obtained results from the SCGNNs have been calculated with interval [0, 1] to solve the SED model with reef ecosystems and conservation estimation by taking 13 numbers of neurons with the statical assessments of training, accreditation, and testing have been used as 77%, 12% and 11%, respectively. The input, output, and hidden layer’s structure of the SED model is shown in

The illustrations based on the SED mathematical system are presented in ^{−11}, 5.8828 × 10^{−11} and 1.6161 × 10^{−13}. The gradient presentations are derived in ^{−08}, 9.570 × 10^{−08} and 9.729 × 10^{−08} for case 1 to 3. These illustrations designate the accuracy of the SCGNNs for the SED mathematical system. The fitting curves performances are shown in

Case | MSE | Gradient | Epoch | Performance | Mu | Time | ||
---|---|---|---|---|---|---|---|---|

Testing | Training | Substantiation | ||||||

1 | 3.809 × 10^{−11} |
3.04 × 10^{−11} |
7.669 × 10^{−11} |
9.98 × 10^{−08} |
68 | 3.04 × 10^{−11} |
1 × 10^{−10} |
2 Sec |

2 | 7.108 × 10^{−11} |
4.62 × 10^{−11} |
5.883 × 10^{−11} |
9.71 × 10^{−08} |
58 | 4.62 × 10^{−11} |
1 × 10^{−10} |
2 Sec |

3 | 1.766 × 10^{−13} |
1.97 × 10^{−13} |
1.616 × 10^{−13} |
9.65 × 10^{−08} |
38 | 1.98 × 10^{−13} |
1 × 10^{−14} |
1 Sec |

The results (reference and obtained) comparisons are presented in ^{−05} to 10^{−06}, 10^{−04} to 10^{−06} and 10^{−06} to 10^{−07} for 1^{st} to 3^{rd} case. The AE for the class ^{−05} to 10^{−07}, 10^{−05} to 10^{−08} and 10^{−07} to 10^{−09}. The AE for the class ^{−05} to 10^{−07}, 10^{−05} to 10^{−06} and 10^{−06} to 10^{−07}. The AE for the class ^{−07} to 10^{−08}, 10^{−06} to 10^{−07} and 10^{−07} to 10^{−09}. Moreover, the AE measures for the category ^{−05} to 10^{−08}, 10^{−05} to 10^{−06} and 10^{−06} to 10^{−08} for 1^{st} to 3^{rd} case of the SED mathematical model. These overlapping of the calculated and reference results as well as the AE values perform the accuracy of the proposed SCGNNs for solving the SED nonlinear mathematical system.

The motive of current investigations is to provide a computational structure using the stochastic procedure based on the scaled conjugate gradient neural networks for the socio-ecological dynamics with reef ecosystems and conservation estimation. The mathematical formulations of the SED using the reef ecosystems and conservation estimation have been presented with five categories, Macroalgae

The designed SCGNNs scheme can be applied in the future to solve the various fluid systems, lonngren-wave networks [