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Task delegation is essential to many applications, ranging from outsourcing of work to the design of routing protocols. Much research in computational trust has been devoted to the generation of policies to determine which agent should the task be delegated to, given the agent's past behaviour. Such work, however, does not consider the possibility of the agent delegating the task onwards, inducing a chain of delegation events before the task is finally executed. In this paper, we consider the process of delegation chain formation, introducing a new algorithm based on quitting games to cater for recursive scenarios. We evaluate our proposal under various network topologies, consistently demonstrating its superiority with respect to recursive adaptations of existing multi-armed bandit algorithms. [ABSTRACT FROM AUTHOR]

In a causal world the direction of the time arrow dictates how past causal events in a variable X produce future effects in Y. X is said to cause an effect in Y , if the predictability (uncertainty) about the future states of Y increases (decreases) as its own past and the past of X are taken into consideration. Causality is thus intrinsic dependent on the observation of the past events of both variables involved, to the prediction (or uncertainty reduction) of future event of the other variable. We will show that this temporal notion of causality leads to another natural spatiotemporal definition for it, and that can be exploited to detect the arrow of influence from X to Y , either by considering shorter time-series of X and longer time-series of Y (an approach that explores the time nature of causality) or lower precision measured time-series in X and higher precision measured time-series in Y (an approach that explores the spatial nature of causality). Causality has thus space and time signatures, causing a break of symmetry in the topology of the probabilistic space, or causing a break of symmetry in the length of the measured time-series, a consequence of the fact that information flows from X to Y. [ABSTRACT FROM AUTHOR]

In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e. networks of subnetworks (layers), by means of the sum of the positive Lyapunov exponents, HKS, a quantity related to entropy. We show that extensivity relies not only on the interplay between the coupling strengths of the dynamics associated to the intra (short-range) and inter (long-range) interactions, but also on the sum of the intra-degrees of the nodes of the layers. For the analytically treated networks of size N, among several other results, we show that if the sum of the intra-degrees (and the sum of inter-degrees) scales as Nθ +1, θ > 0, extensivity can be maintained if the intra-coupling (and the inter-coupling) strength scales as N− θ, when evolution is driven by the maximisation of HKS. We then verify our analytical results by performing numerical simulations in multiplex networks formed by electrically and chemically coupled neurons. [ABSTRACT FROM AUTHOR]

This paper presents a simple and novel approach, based on nonlinear time series analysis of an experimental system, to infer from subtle alteration of the system dynamics the changes caused in the system parameters. Using the acceleration time-series as a measurement of simulated and experimental impact oscillators (serving as a model for the drilling conditions with intermittent contact between the drill- bit and the formation), the systems attractor is reconstructed and characterised. It is shown that the stiffness correlates with the topology of the reconstructed attractor. Non-impacting trajectories form an approximate plane within the three dimensional reconstructed phase-space, and contact with the constraint causes a systematic deviation from the linear subspace, the inclination of which, measured by the statistics of the tangent vector, can be used to infer the stiffness. This relationship between the topology of attractor and the stiffness was also verified experimentally. Based on the developed framework, it is now possible to classify the stiffness of the impacted material from a single variable in a simple way and in real time. [ABSTRACT FROM AUTHOR]

Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations of observability coefficients produce large polynomial functions with a number of terms that become exponentially large with the dimension and the nature of the system. In order to overcome this difficulty, we introduce here a symbolic observability coefficient based on a symbolic computation of the determinant of the observability matrix. The computation of such coefficients is straightforward and can be easily analytically carried out, as demonstrated in this paper for a five-dimensional rational system. [ABSTRACT FROM AUTHOR]

The modern world fully relies on wireless communication. Because of intrinsic physical constraints of the wireless physical media (multipath, damping, and filtering), signals carrying information are strongly modified, preventing information from being transmitted with a high bit rate. We show that, though a chaotic signal is strongly modified by the wireless physical media, its Lyapunov exponents remain unaltered, suggesting that the information transmitted is not modified by the channel. For some particular chaotic signals, we have indeed proved that the dynamic description of both the transmitted and the received signals is identical and shown that the capacity of the chaos-based wireless channel is unaffected by the multipath propagation of the physical media. These physical properties of chaotic signals warrant an effective chaos-based wireless communication system. [ABSTRACT FROM AUTHOR]

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it. [ABSTRACT FROM AUTHOR]

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators. [ABSTRACT FROM AUTHOR]

We investigate the physical modifications caused by a linear filter in a chaotic trajectory. We show that while the filter strongly modifies the topological characteristics of the chaotic signal, it might not alter its information content. We propose a chaos-based communication system that takes advantage of this fundamental characteristic of the dynamics. We devise procedures both to recover all the symbols at the receiver end and to decode the received higher-dimensional filtered chaotic signal by using techniques from the theory of pattern recognition. Our results show that a message bearing chaotic signal can be transmitted over a low bandwidth physical channel and be decoded with a low decoding bit error rate. [ABSTRACT FROM AUTHOR]

This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons. [ABSTRACT FROM AUTHOR]

We find numerically small scale basic structures of homoclinic bifurcation curves in the parameter space of the Chua circuit. The distribution of these basic structures in the parameter space and their geometrical properties constitute a complete homoclinic bifurcation scenario of this system. Furthermore, these structures and the scenario are theoretically demonstrated to be generic to a large class of dynamical systems that presents, as the Chua circuit, Shilnikov homoclinic orbits. We classify the complexity of primary and subsidiary homoclinic orbits by their order given by the number of their returning loops. Our results confirm previous predictions of structures of homoclinic bifurcation curves and extend this study to high order primary orbits. Furthermore, we identify accumulations of bifurcation curves of subsidiary homoclinic orbits into bifurcation curves of both primary and subsidiary orbits. [ABSTRACT FROM AUTHOR]

Basic phenomena in chaos can be associated with homoclinic and heteroclinic orbits. In this paper, we present a general numerical method to demonstrate the existence of these orbits in piecewise-linear systems. We also show that the tangency of the stable and unstable manifolds, at the onset of the chaotic double-scroll attractor, changes the basin boundaries of two α-limit sets. These changes are evidence of homoclinicity in the dynamical system. These basins give complete information about the stable manifolds around the fixed points. We show that trajectories that depart from these boundaries (for backward integration) are bounded sets. Moreover, we also show that the unstable manifolds are geometrically similar to the existing attracting sets. In fact, when no homo- (hetero-)clinic orbits exist, the attractors are ω-limit sets of initial conditions on the unstable manifolds. [Copyright &y& Elsevier]

By using the Chua circuit we present experimental results for the feasibility of a chaotic communication scheme in which large parameter variations are allowed. The parameters are varied along special codimension one directions, on which the topology of chaotic attractors remains roughly invariant. [ABSTRACT FROM AUTHOR]

Periodicity is ubiquitous in nature. In this work, we analyze the dynamical reasons for which periodic windows, that appear in parameter space diagrams, have different shapes and structures. For that, we make use of a dynamical quantity, called spine — the skeleton of the window, in order to explain a conjecture that describes the presence of periodic windows in the parameter space of high-dimensional chaotic systems. [ABSTRACT FROM AUTHOR]

We find the conditions for a chaotic system to transmit a general source of information efficiently. Transmission of information with very low probability of error is possible if the topological entropy of the transmitted wave signal is greater than or equal to the Shannon entropy of the source message minus the conditional entropy coming from the limitations of the channel (such as equivocation by the noise). This condition may not be always satisfied both due to dynamical constraints and due to the nonoptimal use of the dynamical partition. In both cases, we describe strategies to overcome these limitations. [ABSTRACT FROM AUTHOR]

We show differences of the synchronization basins of two Matsumoto-Chua's circuit (operating in either the Ro¨ssler-type attractor regime or the Double-Scroll-type attractor regime), coupled unidirectionally or bidirectionally through a negative feed-back controller. The knowledge of the structure of the synchronization basins allows one to design a communication system robust to imperfections on the setting of the initial condition. [Copyright &y& Elsevier]

Presents a method to rapidly direct a chaotic system to an aimed state or target through a sequence of control perturbations, with few different amplitudes chosen according to the allowed control-parameter changes. Logistic map; Creation and control of orbits; Noise; Double scroll circuit for targeting fluxes; Application of the targeting procedure.

In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher Lyapunov exponent compared to its seed map, and all periodic orbits of any period will be unstable, leading to robust chaos. The technique is tested on several maps from the literature, yielding increased chaotic behavior in all cases, as indicated by comparison of the bifurcation and Lyapunov exponent diagrams of the original and resulting maps. Moreover, the effect of the proposed technique in the problem of pseudo-random bit generation is studied. Using a standard bit generation technique, it is shown that the proposed maps demonstrate increased statistical randomness compared to their seed ones, when used as a source for the bit generator. This study illustrates that the proposed method is an efficient chaotification technique for maps that can be used in chaos-based encryption and other relevant applications. [ABSTRACT FROM AUTHOR]

We show that the degree-degree correlations have a major impact on global synchronizability (GS) of multiplex networks, enabling the specification of synchronizability by only changing the degree-degree correlations of the mirror nodes while maintaining the connection architecture of the individual layer unaltered. If individual layers have nodes that are mildly correlated, the multiplex network is best synchronizable when the mirror degrees are strongly negatively correlated. If individual layers have nodes with strong degree-degree correlations, mild correlations among the degrees of mirror nodes are the best strategy for the optimization of GS. Global synchronization also depend on the density of connections, a phenomenon not observed in a single layer network. The results are crucial to understand, predict, and specify behavior of systems having multiple types of connections among the interacting units. [ABSTRACT FROM AUTHOR]

Chaos-related applications are abundant in the literature, and span the fields of secure communications, encryption, optimization, and surveillance. Such applications take advantage of the unpredictability of chaotic systems as an alternative to using true random processes. The chaotic systems used, though, must showcase the statistical characteristics suitable for each application. This may often be hard to achieve, as the design of maps with tunable statistical properties is not a trivial task. Motivated by this, the present study explores the task of constructing maps, where the statistical measures like the mean value can be appropriately controlled by tuning the map's parameters. For this, a family of piecewise maps is considered, with three control parameters that affect the endpoint interpolations. Numerous examples are given, and the maps are studied through a collection of numerical simulations. The maps can indeed achieve a range of values for their statistical mean. Such maps may find extensive use in relevant chaos-based applications. To showcase this, the problem of chaotic path surveillance is considered as a potential application of the designed maps. Here, an autonomous agent follows a predefined trajectory but maneuvers around it in order to imbue unpredictability to potential hostile observers. The trajectory inherits the randomness of the chaotic map used as a seed, which results in chaotic motion patterns. Simulations are performed for the designed strategy. [ABSTRACT FROM AUTHOR]

Higher-order interactions improve our capability to model real-world complex systems ranging from physics and neuroscience to economics and social sciences. There is great interest nowadays in understanding the contribution of higher-order terms to the collective behavior of the network. In this work, we investigate the stability of complete synchronization of complex networks with higher-order structures. We demonstrate that the synchronization level of a network composed of nodes interacting simultaneously via multiple orders is maintained regardless of the intensity of coupling strength across different orders. We articulate that lower-order and higher-order topologies work together complementarily to provide the optimal stable configuration, challenging previous conclusions that higher-order interactions promote the stability of synchronization. Furthermore, we find that simply adding higher-order interactions based on existing connections, as in simple complexes, does not have a significant impact on synchronization. The universal applicability of our work lies in the comprehensive analysis of different network topologies, including hypergraphs and simplicial complexes, and the utilization of appropriate rescaling to assess the impact of higher-order interactions on synchronization stability. [ABSTRACT FROM AUTHOR]

The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modeling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks by evolving only one layer while keeping other layers fixed. Our main finding is to show the conditions under which the efficiency of convergence to the most optimal structure is almost as good as the case where both layers are rewired during an optimization process. In particular, interlayer coupling strength responsible for the integration between the layers turns out to be a crucial factor governing the efficiency of optimization even for the cases when the layer going through the evolution has nodes interacting much more weakly than those in the fixed layer. Additionally, we investigate the dependency of synchronizability on the rewiring probability which governs the network structure from a regular lattice to the random networks. The efficiency of the optimization process preceding evolution driven by the optimization process is maximum when the fixed layer has regular architecture, whereas the optimized network is more synchronizable for the fixed layer having the rewiring probability lying between the small-world transition and the random structure. [ABSTRACT FROM AUTHOR]

This paper explores the deep-zoom properties of the chaotic k -logistic map, in order to propose an improved chaos-based cryptosystem. This map was shown to enhance the random features of the Logistic map, while at the same time reducing the predictability about its orbits. We incorporate its strengths to security into a previously published cryptosystem to provide an optimal pseudo-random number generator (PRNG) as its core operation. The result is a reliable method that does not have the weaknesses previously reported about the original cryptosystem. [ABSTRACT FROM AUTHOR]

Abstract Information needs to be appropriately encoded to be reliably transmitted over physical media. Similarly, neurons have their own codes to convey information in the brain. Even though it is well-known that neurons exchange information using a pool of several protocols of spatio-temporal encodings, the suitability of each code and their performance as a function of network parameters and external stimuli is still one of the great mysteries in neuroscience. This paper sheds light on this by modeling small-size networks of chemically and electrically coupled Hindmarsh–Rose spiking neurons. We focus on a class of temporal and firing-rate codes that result from neurons' membrane-potentials and phases, and quantify numerically their performance estimating the Mutual Information Rate, aka the rate of information exchange. Our results suggest that the firing-rate and interspike-intervals codes are more robust to additive Gaussian white noise. In a network of four interconnected neurons and in the absence of such noise, pairs of neurons that have the largest rate of information exchange using the interspike-intervals and firing-rate codes are not adjacent in the network, whereas spike-timings and phase codes (temporal) promote large rate of information exchange for adjacent neurons. If that result would have been possible to extend to larger neural networks, it would suggest that small microcircuits would preferably exchange information using temporal codes (spike-timings and phase codes), whereas on the macroscopic scale, where there would be typically pairs of neurons not directly connected due to the brain's sparsity, firing-rate and interspike-intervals codes would be the most efficient codes. [ABSTRACT FROM AUTHOR]

The presence of undesirable dominating signals in geophysical experimental data is a challenge in many subfields. One remarkable example is surface gravimetry, where frequencies from Earth tides correspond to time-series fluctuations up to a thousand times larger than the phenomena of major interest, such as hydrological gravity effects or co-seismic gravity changes. This work discusses general methods for the removal of unwanted dominating signals by applying them to 8 long-period gravity time-series of the International Geodynamics and Earth Tides Service, equivalent to the acquisition from 8 instruments in 5 locations representative of the network. We compare three different conceptual approaches for tide removal: frequency filtering, physical modelling, and databased modelling. Each approach reveals a different limitation to be considered depending on the intended application. Vestiges of tides remain in the residues for the modelling procedures, whereas the signal was distorted in different ways by the filtering and data-based procedures. The linear techniques employed were power spectral density, spectrogram, cross-correlation, and classical harmonics decomposition, while the system dynamics was analysed by state-space reconstruction and estimation of the largest Lyapunov exponent. Although the tides could not be completely eliminated, they were sufficiently reduced to allow observation of geophysical events of interest above the 10 nm s-2 level, exemplified by a hydrology-related event of 60 nm s-2. The implementations adopted for each conceptual approach are general, so that their principles could be applied to other kinds of data affected by undesired signals composed mainly by periodic or quasi-periodic components. [ABSTRACT FROM AUTHOR]

Chemotherapy is a widely accepted method for tumour treatment. A medical doctor usually treats patients periodically with an amount of drug according to empirical medicine guides. From the point of view of cybernetics, this procedure is an impulse control system, where the amount and frequency of drug used can be determined analytically using the impulse control theory. In this paper, the stability of a chemotherapy treatment of a tumour is analysed applying the impulse control theory. The globally stable condition for prescription of a periodic oscillatory chemotherapeutic agent is derived. The permanence of the solution of the treatment process is verified using the Lyapunov function and the comparison theorem. Finally, we provide the values for the strength and the time interval that the chemotherapeutic agent needs to be applied such that the proposed impulse chemotherapy can eliminate the tumour cells and preserve the immune cells. The results given in the paper provide an analytical formula to guide medical doctors to choose the theoretical minimum amount of drug to treat the cancer and prevent harming the patients because of over-treating. This article is part of the themed issue ‘Horizons of cybernetical physics’. [ABSTRACT FROM AUTHOR]

In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The technique consists of adding the remainder of multiple scalings of the map's value for the next iteration, so that the most- and least-significant digits are combined. By appropriate parameter tuning, the resulting map can achieve a higher Lyapunov exponent value, a result that was first proven theoretically and then showcased through numerical simulations for a collection of chaotic maps. As a proposed application of the transformed maps, the encryption of B-spline curves and patches was considered. The symmetric encryption consisted of two steps: a shuffling of the control point coordinates and an additive modulation. A transformed chaotic map was utilised to perform both steps. The resulting ciphertext curves and patches were visually unrecognisable compared to the plaintext ones and performed well on several statistical tests. The proposed work gives an insight into the potential of the remainder operator for chaotification, as well as the chaos-based encryption of curves and computer graphics. [ABSTRACT FROM AUTHOR]

The electric power system is one of the cornerstones of modern society. One of its most serious malfunctions is the blackout, a catastrophic event that may disrupt a substantial portion of the system, playing havoc to human life and causing great economic losses. Thus, understanding the mechanisms leading to blackouts and creating a reliable and resilient power grid has been a major issue, attracting the attention of scientists, engineers, and stakeholders. In this paper, we study the blackout problem in power grids by considering a practical phase-oscillator model. This model allows one to simultaneously consider different types of power sources (e.g., traditional AC power plants and renewable power sources connected by DC/AC inverters) and different types of loads (e.g., consumers connected to distribution networks and consumers directly connected to power plants). We propose two new control strategies based on our model, one for traditional power grids and another one for smart grids. The control strategies show the efficient function of the fastresponse energy storage systems in preventing and predicting blackouts in smart grids. This work provides innovative ideas which help us to build up a robuster and more economic smart power system. [ABSTRACT FROM AUTHOR]

In this work we redefine the concept of biological importance and how to compute it, based on a model of complex networks and random walk. We call this new procedure, theoretical knock-out (KO). The proposed method generalizes the procedure presented in a recent study about Oral Tolerance. To devise this method, we make two approaches: algebraically and algorithmically. In both cases we compute a vector on an asymptotic state, called flux vector. The flux is given by a random walk on a directed graph that represents a biological phenomenon. This vector gives us the information about the relative flux of walkers on a vertex which represents a biological agent. With two vector of this kind, we can calculate the relative mean error between them by averaging over its coefficients. This quantity allows us to assess the degree of importance of each vertex of a complex network that evolves in time and has experimental background. We find out that this procedure can be applied in any sort of biological phenomena in which we can know the role and interrelationships of its agents. These results also provide experimental biologists to predict the order of importance of biological agents on a mounted complex network. [ABSTRACT FROM AUTHOR]

Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains. [ABSTRACT FROM AUTHOR]

We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an “experimental” implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented. [ABSTRACT FROM AUTHOR]

The ability to design a transport network such that commodities are brought from suppliers to consumers in a steady, optimal, and stable way is of great importance for distribution systems nowadays. In this work, by using the circuit laws of Kirchhoff and Ohm, we provide the exact capacities of the edges that an optimal supply-demand network should have to operate stably under perturbations, i.e., without overloading. The perturbations we consider are the evolution of the connecting topology, the decentralization of hub sources or sinks, and the intermittence of supplier and consumer characteristics. We analyze these conditions and the impact of our results, both on the current United Kingdom power-grid structure and on numerically generated evolving archetypal network topologies. [ABSTRACT FROM AUTHOR]

Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rössler oscillators. The Rössler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures. [ABSTRACT FROM AUTHOR]

A correction has been published and is appended to both the HTML and PDF versions of this paper. The error has not been fixed in the paper. [ABSTRACT FROM AUTHOR]

The brain is a complex organ that plays an important role in the control of most functions of the body, such as awareness, thoughts, sensations, movements, speech, and memory. A tumour formed in the brain can affect its ability to accurately and properly perform such functions. In this work, we use two brains with malignant tumours of different sizes before and after surgery. To identify the brain structural topology, we analyse different networks with various configurations and use diagnostic tools to match the network topologies generated by simulations with those obtained from the data. Our results show that the Newman–Watts small-world network best reproduces the topology from the patients with small and large tumours before surgery. Considering two analysed brains, our outcomes suggest that surgery can alter the brain topology from small-world to extended Barabási–Albert scale-free. • Using structural connectivity matrices related to two brains with malignant tumours. • Identifying the brain structural topology by means of various configurations. • Using diagnostic tools to match the network topologies obtained from data. • The surgery radically alters the brain topology. [ABSTRACT FROM AUTHOR]

Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found when a Generating Markov Partition (GMP) is obtained, which is only defined once the unstable and stable manifolds are known with infinite precision and for all times. However, these manifolds usually form highly convoluted Euclidean sets, are a priori unknown, and, as it happens in any real-world experiment, measurements are made with finite resolution and over a finite time-span. The task gets even more complicated if the system is a network composed of interacting dynamical units, namely, a high-dimensional complex system. Here, we tackle this task and solve it by defining a method to approximately construct GMPs for any complex system's finite-resolution and finite-time trajectory. We critically test our method on networks of coupled maps, encoding their trajectories into symbolic sequences. We show that these sequences are optimal because they minimise the information loss and also any spurious information added. Consequently, our method allows us to approximately calculate the invariant probability measures of complex systems from the observed data. Thus, we can efficiently define complexity measures that are applicable to a wide range of complex phenomena, such as the characterisation of brain activity from electroencephalogram signals measured at different brain regions or the characterisation of climate variability from temperature anomalies measured at different Earth regions. [ABSTRACT FROM AUTHOR]

We study the standard nontwist map that describes the dynamic behaviour of magnetic field lines near a local minimum or maximum of frequency. The standard nontwist map has a shearless invariant curve that acts like a barrier in phase space. Critical parameters for the breakup of the shearless curve have been determined by procedures based on the indicator points and bifurcations of periodical orbits, a methodology that demands high computational cost. To determine the breakup critical parameters, we propose a new simpler and general procedure based on the determinism analysis performed on the recurrence plot of orbits near the critical transition. We also show that the coexistence of islands and chaotic sea in phase space can be analysed by using the recurrence plot. In particular, the measurement of determinism from the recurrence plot provides us with a simple procedure to distinguish periodic from chaotic structures in the parameter space. We identify an invariant shearless breakup scenario, and we also show that recurrence plots are useful tools to determine the presence of periodic orbit collisions and bifurcation curves. [ABSTRACT FROM AUTHOR]

In this work a memristive circuit consisting of a first-order memristive diode bridge is presented. The proposed circuit is the simplest memristive circuit containing the specific circuitry realization of the memristor to be so far presented in the literature. Characterization of the proposed circuit confirms its complex dynamic behavior, which is studied by using well-known numerical tools of nonlinear theory, such as bifurcation diagram, Lyapunov exponents and phase portraits. Various dynamical phenomena concerning chaos theory, such as antimonotonicity, which is observed for the first time in this type of memristive circuits, crisis phenomenon and multiple attractors, have been observed. An electronic circuit to reproduce the proposed memristive circuit was designed, and experiments were conducted to verify the results obtained from the numerical simulations. [ABSTRACT FROM AUTHOR]

Recently, much attention has been paid to interpreting the mechanisms for memory formation in terms of brain connectivity and dynamics. Within the plethora of collective states a complex network can exhibit, we show that the phenomenon of Collective Almost Synchronisation (CAS), which describes a state with an infinite number of patterns emerging in complex networks for weak coupling strengths, deserves special attention. We show that a simulated neuron network with neurons weakly connected does produce CAS patterns, and additionally produces an output that optimally model experimental electroencephalograph (EEG) signals. This work provides strong evidence that the brain operates locally in a CAS regime, allowing it to have an unlimited number of dynamical patterns, a state that could explain the enormous memory capacity of the brain, and that would give support to the idea that local clusters of neurons are sufficiently decorrelated to independently process information locally. [ABSTRACT FROM AUTHOR]

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the system's parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this dynamics are the typical response of many natural systems to a periodic external forcing, like e.g. seasonal forcing in ecology and climate sciences. We provide a detailed analysis of tipping phenomena in periodically forced systems and show that, when limit cycles are considered, a transient structure, so-called channel, plays a fundamental role in the transition. Specifically, we demonstrate that trajectories crossing such channel conserve, for a characteristic time, the twisting behavior of the stable limit cycle destroyed in the fold bifurcation of cycles. As a consequence, this channel acts like a 'ghost' of the limit cycle destroyed in the critical transition and instead of the expected abrupt transition we find a smooth one. This smoothness is also the reason that it is difficult to precisely determine the transition point employing the usual indicators of tipping points, like critical slowing down and flickering. [ABSTRACT FROM AUTHOR]

Acoustic communication is a key technology to exchange information underwater, which is of great significance to explore marine resources and to marine defense. The underwater acoustic channel is a time-space-frequency varying channel characterized by serious multipath effect, limited frequency band, complex environmental noises and significant Doppler frequency shift phenomenon, which makes underwater acoustic communication with low Bit Error Rate (BER) to be a challenging task. A novel chaotic spread spectrum acoustic communication method with low BER is proposed in this paper. A chaotic signal, generated by a hybrid dynamical system, is used as a spread spectrum sequence at the transmitter end. At the receiver end, a corresponding chaotic matched filter is used to offset the effect of multipath propagation and noise. The proposed method does not require the complicated equalization and modulation–demodulation technologies that are necessary for conventional acoustic communication. Simulation results show that the proposed method has good anti-interference ability and lower BER as compared to other traditional methods. [ABSTRACT FROM AUTHOR]

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter. [ABSTRACT FROM AUTHOR]

We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (~21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family. [ABSTRACT FROM AUTHOR]