  The Generalized Lotka Voltera (GLV) formalism has been introduced in order to
explain the power law distributions in the individual wealth (w_i (t)) (Pareto
law) and financial markets returns (fluctuations) (r) as a result of the
auto-catalytic (multiplicative random) character of the individual capital
dynamics.
  As long as the multiplicative random factor (lambda) is extracted from the
same probability distribution for all the individuals, the exponent of the
power laws turns out to be independent on the time variations of the average
(<lambda >). This explains also the stability over the past century of
experimentally measured Pareto exponent.
  In contrast to the scaling properties of the single time ("unconditional")
probability distributions, the (auto-)correlations between observables measured
at different times are not correctly reproduced by the original GLV, if the
variance (sigma^2) of $\lambda$ is time independent. In the GLV formalism the
volatility (r^2) auto-correlations decay exponentially while the measurements
in real markets indicate a power law with a very small exponent.
  We show in the present paper that by making the variance of the individual
wealth changes (sigma^2) a function of the market volatility <r^2>, one
correctly reproduces the market volatility long range correlations. Moreover,
we show that this non-trivial feedback loop between the market price volatility
and the variance of the investors wealth leads to non-trivial patterns in the
overall market trends. If the feedback is too strong, it may even endanger the
market stability.
