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The dynamics of Boolean networks with scale-free topology are studied. The existence of a phase transition from ordered to chaotic dynamics, governed by the value of the scale-free exponent of the network, is shown analytically by analyzing the overlap between two distinct trajectories. The phase diagram shows that the phase transition occurs for values of… (More)

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the… (More)

- Maximino Aldana, Enrique Balleza, Stuart Kauffman, Osbaldo Resendiz
- Journal of theoretical biology
- 2007

Living organisms are robust to a great variety of genetic changes. Gene regulation networks and metabolic pathways self-organize and reaccommodate to make the organism perform with stability and reliability under many point mutations, gene duplications and gene deletions. At the same time, living organisms are evolvable, which means that these kind of… (More)

- Elena R. Álvarez-Buylla, Álvaro Chaos, +8 authors Pablo Padilla-Longoria
- PloS one
- 2008

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical… (More)

We investigate the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two-dimensional elements with a ferromagnetic-like interaction. This family is defined to contain under the same framework, among others, the XY-model and the Self-Driven Particles Model introduced by Vicsek et al. Each model is… (More)

- Maximino Aldana, Philippe Cluzel
- Proceedings of the National Academy of Sciences…
- 2003

As biological studies shift from molecular description to system analysis we need to identify the design principles of large intracellular networks. In particular, without knowing the molecular details, we want to determine how cells reliably perform essential intracellular tasks. Recent analyses of signaling pathways and regulatory transcription networks… (More)

The coordinated expression of the different genes in an organism is essential to sustain functionality under the random external perturbations to which the organism might be subjected. To cope with such external variability, the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as to guarantee stability… (More)

- Cristián Huepe, Maximino Aldana
- Physical review letters
- 2004

Intermittent behavior is shown to appear in a system of self-driven interacting particles. In the ordered phase, most particles move in the same approximate direction, but the system displays a series of intermittent bursts during which the order is temporarily lost. This intermittency is characterized and its statistical properties are found analytically… (More)

- Maximino Aldana, Hernán Larralde
- Physical review. E, Statistical, nonlinear, and…
- 2004

We investigate the nature of the phase transition from an ordered to a disordered state that occurs in a family of neural network models with noise. These models are closely related to the majority voter model, where a ferromagneticlike interaction between the elements prevails. Each member of the family is distinguished by the network topology, which is… (More)

- Ilya Shmulevich, Stuart A Kauffman, Maximino Aldana
- Proceedings of the National Academy of Sciences…
- 2005

Two important theoretical approaches have been developed to generically characterize the relationship between the structure and function of large genetic networks: the continuous approach, based on reaction-kinetics differential equations, and the Boolean approach, based on difference equations and discrete logical rules. These two approaches do not always… (More)