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**Journal of Complex Systems**

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**Open Access journal**

ISSN (Print) 2356-7244 - ISSN (Online) 2314-6540

*This journal is no longer being updated because:*

The journal ceased publication in 2016

The journal ceased publication in 2016

**Use of False Nearest Neighbours for Selecting Variables and Embedding**

Parameters for State Space Reconstruction**Abstract:**If data are generated by a system with a d-dimensional attractor,then Takens’ theorem guarantees that reconstruction that is diffeomorphicto the original attractor can be built from the single time seriesin -dimensional phase space. However, under certain conditions,reconstruction is possible even in a space of smaller dimension. Thistopic is very important because the size of the reconstruction spacerelates to the effectiveness of the whole subsequent analysis. Inthis paper, the false nearest neighbour (FNN) methods are revisitedto estimate the optimum embedding parameters and the most appropriateobservables for state space reconstruction. A modification of thefalse nearest neighbour method is introduced. The findings contribute to evidence that the length of the embeddingtime window (TW) is more important than the reconstruction delay timeand the embedding dimension (ED) separately. Moreover, if severaltime series of the same system are observed, the choice of the onethat is used for the reconstruction could also be critical. The resultsare demonstrated on two chaotic benchmark systems.**PubDate:**Mon, 09 Mar 2015 07:08:36 +000

**Some Fixed Point Theorems in Complex Valued b-Metric Spaces****Abstract:**Recently, Azam et al. introduced the notion of complex valued metric spaces and proved fixed point theorems under the contraction condition. Rao et al. introduced the notion of complex valued b-metric spaces. In this paper, we obtain some fixed point results for the mapping satisfying rational expressions in complex valued b-metric spaces. Also, an example is given to illustrate our obtained result.**PubDate:**Mon, 26 Jan 2015 07:57:57 +000

**Studying the Relationship between System-Level and Component-Level**

Resilience**Abstract:**The capacity to maintain stability in a system relies on the components which make up the system. This study explores the relationship between component-level resilience and system-level resilience with the aim of identifying policies which foster system-level resilience in situations where existing incentives might undermine it. We use an abstract model of interacting specialized resource users and producers which can be parameterized to represent specific real systems. We want to understand how features, such as stockpiles, influence system versus component resilience. Systems are subject to perturbations of varying intensity and frequency. For our study, we create a simplified economy in which an inventory carrying cost is imposed to incentivize smaller inventories and examine how components with varying inventory levels compete in environments subject to periods of resource scarcity. The results show that policies requiring larger inventories foster higher component-level resilience but do not foster higher system-level resilience. Inventory carrying costs reduce production efficiency as inventory sizes increase. JIT inventory strategies improve production efficiency but do not afford any buffer against future uncertainty of resource availability.**PubDate:**Thu, 08 Jan 2015 07:36:11 +000

**Group Measures and Modeling for Social Networks****Abstract:**Social network modeling is generally based on graph theory, which allows for study of dynamics and emerging phenomena. However, in terms of neighborhood, the graphs are not necessarily adapted to represent complex interactions, and the neighborhood of a group of vertices can be inferred from the neighborhoods of each vertex composing that group. In our study, we consider that a group has to be considered as a complex system where emerging phenomena can appear. In this paper, a formalism is proposed to resolve this problematic by modeling groups in social networks using pretopology as a generalization of the graph theory. After giving some definitions and examples of modeling, we show how some measures used in social network analysis (degree, betweenness, and closeness) can be also generalized to consider a group as a whole entity.**PubDate:**Tue, 30 Sep 2014 11:19:33 +000

**Dynamic Cournot Duopoly Game with Delay****Abstract:**The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.**PubDate:**Thu, 19 Jun 2014 06:08:39 +000

**Conception of Biologic System: Basis Functional Elements and Metric**

Properties**Abstract:**A notion of biologic system or just a system implies a functional wholeness of comprising system components. Positive and negative feedback are the examples of how the idea to unite anatomical elements in the whole functional structure was successfully used in practice to explain regulatory mechanisms in biology and medicine. There are numerous examples of functional and metabolic pathways which are not regulated by feedback loops and have a structure of reciprocal relationships. Expressed in the matrix form positive feedback, negative feedback, and reciprocal links represent three basis elements of a Lie algebra of a special linear group . It is proposed that the mathematical group structure can be realized through the three regulatory elements playing a role of a functional basis of biologic systems. The structure of the basis elements endows the space of biological variables with indefinite metric. Metric structure resembles Minkowski's space-time (+, −, −) making the carrier spaces of biologic variables and the space of transformations inhomogeneous. It endows biologic systems with a rich functional structure, giving the regulatory elements special differentiating features to form steady autonomous subsystems reducible to one-dimensional components.**PubDate:**Tue, 29 Apr 2014 14:21:00 +000

**Complex Stochastic Boolean Systems: Comparing Bitstrings with the Same**

Hamming Weight**Abstract:**A complex stochastic Boolean system (CSBS) is a complex system depending on an arbitrarily large number of random Boolean variables. CSBSs arise in many different areas of science and engineering. A proper mathematical model for the analysis of such systems is based on the intrinsic order: a partial order relation defined on the set of all binary -tuples of 0s and 1s. The intrinsic order enables one to compare the occurrence probabilities of two given binary -tuples with no need to compute them, simply looking at the relative positions of their 0s and 1s. Regarding the analysis of CSBSs, the intrinsic order reduces the complexity of the problem from exponential ( binary -tuples) to linear ( Boolean variables). In this paper, using the intrinsic ordering, we compare the occurrence probabilities of any two binary -tuples having the same number of 1-bits (i.e., the same Hamming weight). Our results can be applied to any CSBS with mutually independent Boolean variables.**PubDate:**Mon, 24 Mar 2014 07:31:40 +000

**A Small Morris-Lecar Neuron Network Gets Close to Critical Only in the**

Small-World Regimen**Abstract:**Spontaneous emergence of neuronal activity avalanches characterized by power-law distributions is known to occur in different types of nervous tissues suggesting that nervous systems may operate at a critical regime. Here, we explore the possible relation of this dynamical state with the underlying topology in a small-size network of interconnected Morris-Lecar neurons. Studying numerically different topological configurations, we find that, very close to the efficient small-world situation, the system self-organizes near to a critical branching process with observable distributions in the proximity of a power law with exponents similar to those reported in the experimental literature. Therefore, we conclude that the observed scaling is intimately related only with the small-world topology.**PubDate:**Thu, 07 Nov 2013 08:57:16 +000

**Weakly Compatible Maps Using E.A. and (CLR) Properties in Complex Valued**

-Metric Spaces**Abstract:**We introduce the notion of complex valued -metric spaces and prove common fixed point theorems for weakly compatible maps along with E.A. and (CLR) properties in complex valued -metric spaces.**PubDate:**Wed, 30 Oct 2013 11:03:03 +000

**Common Fixed Point Theorems for a Rational Inequality in Complex Valued**

Metric Spaces**Abstract:**We prove a common fixed point theorem for a pair of mappings. Also, we prove a common fixed point theorem for pairs of self-mappings along with weakly commuting property.**PubDate:**Thu, 24 Oct 2013 15:09:33 +000

**About Evaluation of Complex Dynamical Systems****Abstract:**Methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system out of given class of equivalent systems, system’s timeline behaviour analysis on the basis of versatile multicriteria, and multilevel analysis of behaviour of system's elements.**PubDate:**Wed, 09 Oct 2013 10:55:19 +000

**Diffusion Models for Information Dissemination Dynamics in Wireless**

Complex Communication Networks**Abstract:**Information dissemination has become one of the most important services of communication networks. Modeling the diffusion of information through such networks is crucial for our modern information societies. In this work, novel models, segregating between useful and malicious types of information, are introduced, in order to better study Information Dissemination Dynamics (IDD) in wireless complex communication networks, and eventually allow taking into account special network features in IDD. According to the proposed models, and inspired from epidemiology, we investigate the IDD in various complex network types through the use of the Susceptible-Infected (SI) paradigm for useful information dissemination and the Susceptible-Infected-Susceptible (SIS) paradigm for malicious information spreading. We provide analysis and simulation results for both types of diffused information, in order to identify performance and robustness potentials for each dissemination process with respect to the characteristics of the underlying complex networking infrastructures. We demonstrate that the proposed approach can generically characterize IDD in wireless complex networks and reveal salient features of dissemination dynamics in each network type, which could eventually aid in the design of more advanced, robust, and efficient networks and services.**PubDate:**Wed, 04 Sep 2013 10:26:02 +000

**Synchronization of Nonidentical Coupled Phase Oscillators in the Presence**

of Time Delay and Noise**Abstract:**We have studied in this paper the dynamics of globally coupled phase oscillators having the Lorentzianfrequency distribution with zero mean in the presence of both time delay and noise. Noise maybe Gaussian or non-Gaussian in characteristics. In the limit of zero noise strength, we find thatthe critical coupling strength (CCS) increases linearly as a function of time delay. Thus the roleof time delay in the dynamics for the deterministic system is qualitatively equivalent to the effectof frequency fluctuations of the phase oscillators by additive white noise in absence of time delay. But for the stochastic model, the critical coupling strength grows nonlinearly with the increase ofthe time delay. The linear dependence of the critical coupling strength on the noise intensity alsochanges to become nonlinear due to creation of additional phase difference among the oscillatorsby the time delay. We find that the creation of phase difference plays an important role in thedynamics of the system when the intrinsic correlation induced by the finite correlation time of thenoise is small. We also find that the critical coupling is higher for the non-Gaussian noise comparedto the Gaussian one due to higher effective noise strength.**PubDate:**Sun, 01 Sep 2013 11:47:14 +000

**Bluffing as a Rational Strategy in a Simple Poker-Like Game Model****Abstract:**We present a simple adaptive learning model of a poker-like game, by means of which we show how a bluffing strategy emerges very naturally and can also be rational and evolutionarily stable. Despite their very simple learning algorithms, agents learn to bluff, and the most bluffing player is usually the winner.**PubDate:**Tue, 04 Jun 2013 14:03:00 +000