Visual Representation of the Butterfly Effect
In H. G. Wells' novel, The Time Machine, the Time Traveler goes thousands of years into the future and interacts with a futuristic society of presumably our descendants. The Eloi and the Morlocks have evolved over the course of thousands of years, and any trace of modern society is mostly dissolved. Everything concerning time was intact for the majority of the book and there was no paradox because the time traveler was moving forward, but when the time traveler finds his machine again, we run into some problems that involve the butterfly effect. When the Time Traveler regains control of his machine he goes further into the future and any paradox is initially avoided. The problem arises when he returns to his own time. Because of his brief actions after returning to Victorian England, we can ask ourselves the question; do the Morlocks and Eloi continue to exist in the theoretical universe of the Time Traveler?
The Butterfly Effect and Chaos Theory
The theory of the Butterfly effect was first coined by a meteorologist, Edward Lorenz. Lorenz was in the process of using the new computer technology at the time to accurately predict long term weather patterns. At first his results were promising, however, he quickly discovered that even a slight change in any variable resulted in an increasingly complicated degree of chaos as time progressed.
From his equations and this observation, he drew the name, saying that a simple disturbance from a butterfly's wings could potentially be linked to a major weather event in other parts of the world such as hurricanes or tornado. In a similar way, Chaos Theory states essentially the same concept as stated in Chaos Theory in Strategy Research, specifically saying, "The premise of chaos theory is that systems are located in the hub of chaotic galaxy. The interactions of the systems and their components generate outcome, but the outcome is unpredictable..." 
The article continues on to explore the Butterfly Effect and Chaos Theory in many situations, ranging from social, natural, mathematical, and economic. The Chaos Theory in time travel is not something we can research with testable results, so to see the results of small changes, many researchers like the authors of Chaos Theory in Strategy Research observe these effects in other aspects of life like those explained earlier. The article goes on to analyze the important of small choices in many areas from economics to literature through changes that weren't necessarily mandated from companies or individuals. We are able to observe these changes and predict the alternative outcomes of decisions made in the present. The article, A simple guide to chaos and complexity, goes deeper into the Chaos Theory and the Butterfly Effect a it observes the importance of "critical phenomena". The ideas of critical phenomena reinforces that a small input into a system can yield varied results. 
This concept, when applied to time travel, can be applied to the assumptions that a small change in the past can yield vastly different results of futures. Ray Bradbury used this theory and applied to time travel in the short story, The Sound of Thunder, in which the future is forever altered by the simple action of stepping on a butterfly.
The premise of the butterfly effect as it relates to time travel is that whenever you travel backwards in time and alter anything, it has the potential to forever alter the future in unforeseeable ways. The farther you go back in time, the more evident these effects are upon returning to the present. For example, if you went back one day in time and stepped on a butterfly, the change once returning to the present would not be that significant. However, traveling millions or even thousands of years into the past would drastically affect the present upon return. This is explained expertly in The Sound of Thunder when the tour guide tell the hunters that anything they alter has the potential to completely change the future. By killing a mouse millions of years ago, you have eliminated all possible relatives of that mouse and therefore affected the entire ecosystem that is dependent on mice for food. This in turn effects countless other things, potentially altering the fabric of what was the present. We are able to apply Bradbury's fictional story and see how these effects are evident in everyday life.
The Time Traveler's Mistake
You now may be asking, "But wait, what bearing does this have on the Time Traveler, Eloi, and the Morlocks? The Time Traveler went forward in time, not backwards." The only way to completely avoid the butterfly effect, is to never travel backwards in time. For the most part the Time Traveler does not break this rule. For most of his journey, he travels further and further into the future. The butterfly effect began as soon as he returned to his own time. Similar to the traveler's journey in Bradbury's "The Sound of Thunder", the Time Traveler returned back from his furthest point in the future, far enough to have a significant difference on the events he has both witnessed and took part in in the time of the Eloi and Morlocks. In "The Sound of Thunder", all the traveler had to do was disturb a small shrub to be in danger of the butterfly effect. When looking at the Time Traveler's action after he returned to England, he shared his detailed memories of the future with his friends and colleagues. While most of them didn't believe him, the idea was still planted in their mind that the Eloi and the Morlocks may exist, especially in the mind of the narrator who believes the Time Traveler. Most of them will certainly share their knowledge with other people therefore spreading the idea of the future even if it is presented as a crazy and delusional tale, it will cause the listener to think about man's destiny, and whether he does it consciously or subconsciously, the listener will make choices and actions that have been influenced by the ideas or "fables" of the future. Thus in turn the ripple of the Butterfly Effect propagates through time and it has the potential to completely change the destiny, biology, and social structure of the Eloi and Morlock societies. At this point it can be argued that they are no longer the same beings that the Time Traveler witnessed or interacted with. Ironically, after the Time Traveler shares his knowledge, even if he wanted to go back, the Eloi and Morlocks would not be the same if they existed in their original state at all.
The Butterfly Effect in Other Works of Science Fiction
Although I am sure that there are many occurrences of this effect portrayed in multiple different works of science fiction, perhaps the most relevant occurrence to this situation appears in Star Trek - Next Generation, Season 3 Episode 15. This episode is unique because it gives us a perspective into what the Eloi and Morlocks might have experienced during the Time Traveler's visit. As a brief summary of the episode, the Enterprise (NCC-1701-D) approaches what appears to be a temporal rift that connects the crew with another ship that has come through it, only from 22 years in the past. The other ship is the older version of the Enterprise (NCC-1701-C to be exact). It was fleeing a battle with the Romulans and was tasked with defending a Klingon outpost. At this point, time is distorted, and the crew of the new Enterprise (NCC-1701-D) enters onto a timeline in which they have been at war with the Klingons for years because the old Enterprise was not there to defend the Klingon outpost on the other side of the rift 22 years in the past. The crew has no knowledge that their timeline has altered except for a crew member, Guinan, who has another sense that something isn't right. The crew interact and eventually determine that the old Enterprise needs to return to the past to try to resolve the conflict that the new timeline has presented. After the old Enterprise returns, and presumably the mission is complete, the timeline shifts again, back the original peaceful mission of the Enterprise (NCC-1701-D). This example related perfectly back to the Eloi and Morlocks, because in this sense, they are the new version of the Enterprise. They are on a specific timeline when the time traveler arrives. When he returns, it is entirely possible that the Eloi and Morlocks experience a timeline shift due to the butterfly effect when the Time Traveler returns to his own time. It's possible that they have shifted unknowingly onto another timeline. This could be as drastic as the fabric of their society changing or them never existing at all. own time. It's possible that they have shifted unknowingly onto another timeline. This could be as drastic as the fabric of their society changing or them never existing at all.
After exploring the possibilities and researcher to back up the Butterfly Effect, it may be entirely possible that the Eloi and Morlocks no longer exist in the same sense because of the small changes made in the past. Much of the research that has been conducted backs up the Butterfly Effect and Chaos theory, however there is a key aspect missing. We have no way to test the Butterfly Effect with reference to Time Travel. Time is still a constant that continues to elude us and it may behave in ways that we have not yet been able to understand. We also have to ask the question, would we even be able to recognize the changes because we would have shift on our time lines. For now, this remains just a theory when it comes to time travel, however if our research is ever able to cover this topic and is consistent with the research we already have, our future will undoubtable look much different than the fiction of the Eloi and Morlocks.