Advances in Complex Systems

The current interest in complex networks is a part of a broader movement towards research on complex systems. Motivation of this work raises the two challenging questions: (i) Are real networks fundamentally random preferential attached without any deterministic attachment for both un-weighted and weighted networks? (ii) Is there a coherent physical idea and model for unifying the study of the formation mechanism of complex networks? To answer these questions, we propose a harmonious unifying hybrid preferential model (HUHPM) to a certain class of complex networks, which is controlled by a hybrid ratio, d/r, and study their behavior both numerically and analytically. As typical examples, we apply the concepts and method of the HUHPM to un-weighted scale-free networks proposed by Barabasi and Albert (BA), weighted evolving networks proposed by Barras, Bartholomew and Vespignani (BBV), and the traffic driven evolution (TDE) networks proposed by Wang et al., to get the so-called HUHPM-BA, HUHPM-BBV and HUHPM-TDE networks. All the findings of topological properties in the above three typical HUHPM networks give certain universal meaningful results which reveal some essential hybrid mechanisms for the formation of nontrivial scale-free and small-world networks.

A new evolving network based on the scale-free network of Barabási and Albert (BA) is studied, and the accelerated attachment of new edges is considered in its evolving process. The accelerated attachment is different from the previous accelerated growth of edges and has two particular meanings in this paper. One is that a new vertex with the edges is inserted into the network with acceleration at each time step; the other is that, with a given probability, some additional edges are linked with the vertices in proportion to the number of their obtained edges in the latest evolving periods. The new model describes the cases of those complex networks with a few exceptional vertices. The attachment mechanism of the new adding edges for these vertices does not follow the preferential attachment rule. Comparing with the linear edge growth model, the characteristics of the accelerated growth model are studied theoretically and numerically. We show that the degree distributions of these models have a power law decay and the exponents are larger than that of the BA model. We point out that the characteristics of the exceptional vertices and the aging vertices in an aging network are not identical. The reasons for neglecting this attachment in most of evolving networks are also summarized.

Previous studies on network topology of artificial gene regulatory networks created by whole genome duplication and divergence processes show subgraph distributions similar to gene regulatory networks found in nature. In particular, certain network motifs are prominent in both types of networks. In this contribution, we analyze how duplication and divergence processes influence network topology and preferential generation of network motifs. We show that in the artificial model such preference originates from a stronger preservation of protein than regulatory sites by duplication and divergence. If these results can be transferred to regulatory networks in nature, we can infer that after duplication the paralogous transcription factor binding site is less likely to be preserved than the corresponding paralogous protein.

We investigate the dynamics of a single-species model with birth pulses and pulse harvesting in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact 1-period solution of the system whose birth function is a Ricker or Beverton–Holt function and obtain the threshold conditions for their stability. Further, we show the effects of the time of pulse harvesting on the maximum annual-sustainable yield. Our results show that the best time for harvesting is immediately after the birth pulses. Numerical simulation results also show that birth pulses and pulse harvesting make the single-species model in a polluted environment we consider more complex, and the system is dominated by periodic and chaotic solutions.

The present paper studies the naturally observed phenomenon of population fluctuation in the context of a minimal plankton model. The analysis of the basic model reveals asymptotic stable behavior that is unable to explain any kind of population outburst. We introduce the nonuniform spatial distribution of plankton by considering physical diffusion of the species concerned. The resulting reaction-diffusion equation model is first analyzed with constant diffusivity and then with variable diffusivity for the zooplankton. The model with variable diffusivity is analyzed by using Floquet theory. In both cases, the model is seen to exhibit stable behavior. Finally, we study another characteristic feature of any ecological population, namely, environmental fluctuations. We achieve this by perturbing the growth rate of phytoplankton and death rate of zooplankton by using colored noise. The resulting model is analyzed by evaluating the spectral density functions. It is observed that the stochastic model can generate a large fluctuation in population concentration for high amplitude driving forces.

In this paper, we investigate the extinction, permanence and dynamic complexity of the two-prey, one-predator system with Ivlev's functional response and impulsive perturbation on the predator at fixed moments. Conditions for the extinction and permanence of the system are established via the comparison theorem. Numerical simulations are carried out to explain the conclusions we obtain. Furthermore, the resulting bifurcation diagrams clearly show that the impulsive system takes on many forms of complexity including period-doubling bifurcation, period-halving bifurcation, and chaos.

The conventional wisdom derived from the two-step flow theory suggests that opinion leaders have great influence on their followers. However, it has been difficult for social scientists to measure and describe the extent to which political opinion leaders influence voters, especially when voters today access multiple information sources like communication networks and self-selected news media. This paper fills this gap by using agent-based modeling to represent what the two-step flow theory describes about opinion leader influence and refines the theory based on the findings. First, opinion leader influence does not diffuse to the public without homogeneous communication networks. Second, opinion leader influence usually does not diffuse widely to the public because it inevitably faces resistance from self-strengthening communication networks.

We explore the possibilities of enforcing and preventing consensus in continuous opinion dynamics that result from modifications in the communication rules. We refer to the model of Weisbuch and Deffuant, where n agents adjust their continuous opinions as a result of random pairwise encounters whenever their opinions differ not more than a given bound of confidence ε. A high ε leads to consensus, while a lower ε leads to a fragmentation into several opinion clusters. We drop the random encounter assumption and ask: How small may ε be such that consensus is still possible with a certain communication plan for the entire group? Mathematical analysis shows that ε may be significantly smaller than in the random pairwise case. On the other hand, we ask: How large may ε be such that preventing consensus is still possible? In answering this question, we prove Fortunato's simulation result that consensus cannot be prevented for ε > 0.5 for large groups. Next, we consider opinion dynamics under different individual strategies and examine their power to increase the chances of consensus. One result is that balancing agents increase chances of consensus, especially if the agents are cautious in adapting their opinions. However, curious agents increase chances of consensus only if those agents are not cautious in adapting their opinions.

The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper, we propose an agent-based model to show that randomly distributed social behavior by way of local interaction converges to a state with a multimodal distribution of behavior. This can be interpreted as a coexistence of different social norms, a result that goes beyond previous investigations. The model is discrete in time and space, behavior is characterized in a continuous state space. The adaptation of social behavior by each agent is based on attractive and repulsive forces caused by friendly and adversary relations among agents. The model is analyzed both analytically and by means of spatio-temporal computer simulations. It provides conditions under which we find convergence towards a single norm, coexistence of two opposing norms, and coexistence of a multitude of norms. For the latter case, we also show the evolution of the spatio-temporal distribution of behavior.