“Chaos” is a challenging process. In contrast, it would be far simpler to enumerate the qualities of a “chaotic” system than it is to establish a comprehensive description of chaos. A chaotic dynamical system is one that exhibits sensitive reliance on beginning circumstances on a confined consistent set. A chaotic strategy to a predictable formula is one whose outcome is particularly sensitive to beginning parameters (small variations in beginning parameters result in large variations in findings) and those whose progression across phase space has been quite random. Its unique concepts and high-speed computation have yielded novel insights into the behaviour of complicated processes and shown startling conclusions, perhaps in the easiest non-linear frameworks. Non-linear functions can be performed by “bifurcation-points,” or locations where the process, as it were, sits on such a knife-edge and may abruptly change its intrinsic behaviour. System behaviour can occasionally become exceedingly irregular and chaotic. In such instances, even based on the system’s whole history, predicting its future behaviour becomes difficult. The system’s behaviour varies wildly from one moment to the next; furthermore, it could be indefinitely susceptible to any exterior fluctuation variation. The electroencephalogram (EEG) is one example of a nonlinear signal.

**Elman-Chaotic Optimization for Epilepsy Risk Level Optimization**

To analyze the use of the Elman-chaotic optimization model to examine the optimization of fuzzy outcomes in the detection of epilepsy risk levels using EEG recordings. Fuzzy approaches are used as a primary level predictor to define the epilepsy risk levels. The fuzzy outputs are coded and fed into a chaotic optimization model, which incorporates the central tendency measure as a major approach for determining the epileptic patient’s risk level. For optimal classification, the chaotic optimized output is passed to Elman neural networks. The EEG data utilized in the analysis were obtained from 10 epileptic patients who were being evaluated and treated at the Neurology subdivision of Sri Ramakrishna hospital in tamilnadu, India.

**Chaotic Optimization**

One of the most notable characteristics of a chaotic mechanism is that it seems to exhibit unexpected behaviour, which is referred to as deterministic disorder. The unstable performance of a chaotic process suggests that it does not resist output disturbances but nevertheless reacts significantly. A chaotic system demonstrating such dynamics is extremely complicated since it never replicates and continues to illustrate the influence of disruptions. Let us examine the well-known Poincare equation, often known as the Population equation.

This iterative task doesn’t often immediately become chaotic, but rather progresses from the phase of convergence to such a specified variable to bifurcation, followed by more bifurcation. The approach lacks coherence and responsiveness to beginning circumstances because it’s the most significant aspect of Chaos. In the Poincare equation discussed above, A is a persistent whose score determines the system’s performance. The recursion is determined by the choice of a starting value a0 between 0 and 1. A significantly modified version of the Poincare model is expressed as

The forcing function is the last element in the above equation. The constant could be modified, but an effort must be made to ensure that the equation remains inside the chaotic region. The input values for the improved Poincare equation are simply categorized numerical values from the fuzzy output system. We deploy a third-order differential plot to examine the differences and degree of conceptual chaos, which is a graph plot of (a(n+1)-a(n)) versus (b(n+1)-b(n)) versus (c(n+1)-c(n)). It provides a clearer picture of how the points have been widely scattered or grouped near the source. The Central Tendency Measure (CTM) is a method for quantifying the amount of uncertainty in third-order differential maps as represented following figure. The CTM is obtained by dividing the total amount of points by a circular circle of radius ‘r’.

**Elman Neural Network**

The Elman neural network can be defined as a partly recurrent network or a basic recurrent network since the hidden layer’s outputs are permitted to reflect onto itself via a buffer layer known as the context layer. Elman networks may learn, identify, and develop temporal and spatial patterns as a result of this feedback. Each hidden layer is linked to a single context layer neuron by a persistent weight of one. As a result, the context layer is a form of replica of the concealed layer’s state from one instant ago. As a result, the number of context neurons equals the number of hidden units. In general, the activation functions of output, context neurons, and inputs are linear, however hidden neurons possess sigmoidal activation gatherings.