Introduction

Keywords

Limits; crises; complex behavior

In November 1997 the financial crisis of that time had already started in Mexico and the Asian Tigers were having problems. Moreover, Russia was entering the crisis situation too. The bifurcation related to the change from one state to the other—in the case of stock exchange, from “sell” to “buy” is an indication of a change in the traders’ collective behavior that is triggered by small changes of perceived parameters’ evolution. The euphoria of a seemingly endless exponential growth of some financial instruments is replaced suddenly by the sorrow of a saturation followed by abandoning the allocation of money to some instruments and the shift toward others.

There is an important message here that is the fact that people have in their minds some given states and external information is almost unconsciously interpreted as either going toward one or the other, without anything in between. This behavior is produced by some entities of the mind having similar properties with genes whose conceptualization had been done by Dawkins who also coined the name “meme” for them.

Actually, in a booklet titled “Modern Money Mechanics,” the Federal Reserve Bank of Chicago says: “What, then, makes these instruments—checks, paper money, and coins—acceptable at face value in payment of all debts and for other monetary uses? Mainly, it is the confidence people have that they will be able to exchange such money for other financial assets and real goods and services whenever they choose to do so. This partly is a matter of law; currency has been designated “legal tender” by the government—that is, it must be accepted.”

As we see the basis of money use is about credibility, a concept that relates to people’s minds and this is based on memes dynamics. We will explain more of this in what follows related to the penetration of financial instruments (portfolio components) used in the cultural niches of the financial system.

Application of the notion of meme in the financial environment in relation to the financial instruments leads to the idea of a cultural niche (in the sense of Popper) of financial instruments associated to memes. At each moment in time there are several instruments in the niche but, dynamically, one of them has the tendency to occupy the niche in a logistic way—that is, until it saturates and decays while another instrument takes its place as dominant.

Logistic penetration was used for biological species in competition by Verhulst (1838) and for the penetration of technologies (Marchetti and Nakicenovic’s 1978 work at International Institute for Applied Systems Analysis, IIASA, is relevant), as well as Sornette and Cauwels (2012) and others in looking at the development of Internet companies, for example.

By contrast to Malthus (1798), who advocated the exponential growth of the population in a world where resources were not available with the same speed, Verhulst (1838) had introduced the notion of saturation, given by the limit of the environment where species are in competition. The fact that we live in a world having limits has then been discussed by various economists, among which we mention Kenneth Ewart Boulding (1966) who said:

Later on he concludes:

Going along with Ramos-Martín and Ortega-Cerdà we may say that over half a century ago, Schumpeter (1949) understood nonlinear evolutionary development and discontinuity by means of his theory of creative destruction. This idea has been later named “punctuated equilibrium” by some analysts (Gowdy, 1994), using the same term that is in use in paleontology to describe this stepwise evolution (Eldredge and Gould, 1972; Gould and Eldredge, 1993).

One way of analyzing the existence of this discontinuity is by means of a phase diagram. This methodology has been used in the case of CO2 emissions (Unruh and Moomaw, 1998), and in the case of energy intensity (De Bruyn, 1999; Ramos-Martín 1999, 2001). The phase diagrams are intended to show whether the evolution of certain variables, over time, is stable (even dynamically stable) or divergent. Thus, one may find if there are attractor points or not. If so, we can check how persistent are those attractors as well as the magnitude of the fluctuations around them (Unruh and Moomaw, 1998). In what follows we will show that there is a phase change behavior resulting from the penetration of memes associated to financial instruments.

A potential approach is a time-evolving space in which we monitor the evolution of the variable. This representation allows us to see whether we are facing a “punctuated equilibrium”-like behavior or not. If we are, then we will see how the variable concentrates around certain attractors. If not, the evolution of the variable will be different, showing a more complex, possibly discontinuous, behavior. This means that in the process of development, we should focus empirical research on identifying the attractor points and the system evolution trajectory from one to the other.

This situation leads to a series of “bifurcation” points (Prigogine, 1987), in which, for given boundary conditions, there are several stable solutions. Following Faber and Proops (1998) a “bifurcation may occur when the stable equilibrium for a dynamic system is sensitive to changes in the parameters of the system.” Thus, when the parameter goes beyond a critical threshold, the system becomes sensitive to sudden change and therefore unstable. In this case, tiny perturbations may trigger drastic changes (Dalmazzone, 1999), leading to a set of new different stable equilibriums to which the system might eventually flip. We have just mentioned some authors; actually the literature has developed various examples of nonlinear behavior.

There is a further step to the process, that is, the decision to finance each instrument that is taken by the decision makers in the banks (or other financial entities), which are generally called the markets. This is dependent on the perception by the decision maker of the financial instruments’ dynamic, seen as memes in a niche. The transition probabilities of the master equation of the process are determined by the logistic behavior, bringing a similarity to the Ising process in physics. The decision process is described by the stationary solution of the associated Fokker–Planck equation that shows bifurcation.

This further allows us to represent the behavior of the decision to allocate money to financial instruments in a three-dimensional space described as a cusp catastrophe in Rene Thom’s terminology. The decision is seen as a trajectory that may have a smooth evolution, or a discontinuous one, when passing from a fold to another. The discontinuous case means that a given instrument will not be financed any longer or, in other words, that a meme will have reached saturation in the niche and the decision maker will abandon allocating money to that financial instrument.

If we look back, one may see “dot com’s” were like this, “housing” was like this, as well as other various crises in history as nicely described by Reinhart and Rogoff (2009).

A profound insight into the crisis dynamics was done by Galbraith (1994). His phrase “Financial genius is before the fall” is a synthesis of the process.

He identified both the upward-going phase (that we call exponential growth) and the sudden end (which we describe as a discontinuous decision resulting from saturation in the logistic penetration of the dominant financial instrument). On the upward trend he said:

He also coined the dynamics of the sudden end of the euphoria: