What are the implications of deterministic chaos: useful or detrimental? I am new to the concept of chaos theory and as a layman I am struggling to understand what is the significance and implication of chaos in ecological systems such as the chaotic predator prey model. I have understood how to know that a system is chaotic but I do not yet understood why it is advantageous or if it is problematic in terms of biological/ecological models. I have read several papers the important ones being "Chaos in low-dimensional Lotka–Volterra models of competition" and "Bifurcations and chaotic dynamics in a 4-dimensional competitive Lotka–Volterra system". But I failed to capture what happens when such ecological systems become chaotic-- does it mean death of a species or stability. In this regard I would be grateful if somebody could help in clarifying these doubts and confusions with an intuitive answer:

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*Is chaos a special kind of stable, equilibrium state?


*What is the implication of appearance of chaos and disappearance of chaos in such ecological models?
 A: 
1. Is chaos a special kind of stable, equilibrium state?

If the system has a chaotic attractor, then chaos in this system is dynamically stable, which means this behavior will persist against small perturbations. Beware though - in some, especially old texts, chaotic behavior is called "unstable" for being irregular.

what happens when such ecological systems become chaotic - does it mean death of a species or stability?

In a population dynamics model the death/extinction of a species $x$ simply means that from then on $x=\text{const.}=0$, which is a regular steady state, not a chaotic one.

2. What is the implication of appearance of chaos and disappearance of chaos in such ecological models?

A system (biological or not) being chaotic only means that its behavior is irregular and exponentially sensitive to small changes.
The biological consequences of such behavior are model specific. For instance, one could conjecture that, by being irregular, the size of the population might be out of sync with the seasons - which could be detrimental for the species if a large population arises in a low-resource period.
More concretely, this paper mentions:

a range of more specific possible biological functions for chaos have since been proposed, including potentially maximizing the information processing capacity of both neural systems and gene regulatory networks, enabling multistable perception, allowing neural systems to flexibly transition between different activity patterns, and boosting cellular survival rates through the promotion of heterogeneous gene expression. [...]
a model of white blood cell concentrations in chronic granulocytic leukemia can display varying levels of chaos, and knowing how chaotic those concentrations are in actual leukemia patients could have important implications for health outcomes. As another example, models of the human cortex predict that macro-scale cortical electrodynamics should be weakly chaotic during waking states and should be strongly chaotic under propofol anesthesia; if this prediction is true, then detecting changing levels of chaos in large-scale brain activity could be useful for monitoring depth of anesthesia and for basic anesthesia research.

A: When considering the consequences of chaos on real systems, you first needs to consider to what you are comparing it and what your scientific context is. There are two important contexts:
Understanding given real dynamics
In this context, the most interesting alternative to chaos is not a regular dynamics (fixed point or periodic) but a stochastic one.
The dynamics of most ecological systems falls into one of the following categories:

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*Convergence to an equilibrium, be it with all populations surviving¹ or not.


*Regular oscillations in response to an external driver, e.g., seasons.


*Irregular oscillations, i.e., with no clear frequency. A big open question is whether these oscillations are primarily chaotic (i.e., deterministic) or just noise (stochastic), where the latter can be just noisy oscillations around an equilibrium or periodic dynamics made irregular by noise. Of course the answer could depend on the system, but so far there are only a few disputed claims for a few systems.
The first two cases are generally well understood and clearly not chaotic. In the latter case, the question can be rephrased as: Is the dynamics is primarily deterministic? If the answer is yes, we can model, predict, and control the dynamics to some extent; otherwise we mostly cannot. The answer may also help to predict how the dynamics behaves in response to parameter changes (e.g., climate change): A chaotic oscillation can suddenly transition to some other kind of dynamics, a stochastic system is less likely to do that (though there are such phenomena like stochastic resonance).
¹ Which is called stable in ecology. Mind that in the context of dynamical systems stable means something different, e.g., the extinction of all populations is a stable in the dynamical sense.
Understanding the effect of parameter changes on a model
A common type of study investigates the impact of a control parameter (e.g., temperature, nutrient influx, pH) on the dynamics of a model system, usually a deterministic one.
Typically, the dynamics changes between an equilibrium, periodic and chaotic one in bifurcations and other sudden transitions.
The most important transitions in this context are the ones where the abundance of some population drastically in- or decreases (tipping points) or oscillations arise, be they periodic or chaotic. As far as I can tell, transitions between chaos and regular oscillations (of comparable amplitude) are not of that big interest. There may be exceptions though, e.g., if the system in question drives another system. There are some speculations that chaos may act as an ecologically stabilising factor, but so may regular oscillations.
