Display Complex Dynamics Research Articles

A new chaotic Hopfield neural network and its synthesis via parameter switchings

In this paper, we present a new chaotic attractor in Hopfield neural network. Numerical experiments show that the presented Hopfield neural network can display complex dynamics by changing the self-connection weight. Surprisingly, coexistence of a chaotic attractor and a limit cycle is found in this system, which means, the system can exhibit a chaotic attractor or a limit cycle according to different initial values, and this phenomenon is never reported before. We give a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps. Finally, synthesis of the chaotic attractor is studied via parameter switching and a numerical example illustrates the effectiveness of this method.

Dynamic noise, chaos and parameter estimation in population biology

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models such as multi-strain dynamics to describe the virus-host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

Synchronization and emergence in complex systems

We show how novel behaviour can emerge in complex systems at the global level through synchronization of the activities of their constituent units. Two mechanisms are suggested for the emergence, namely non-diffusive coupling and time delays. In this way, simple units can synchronize to display complex dynamics, or conversely, simple dynamics may arise from complex constituents.

Attractor Nets, Series I: Notes Toward a New Theory of Mind, Logic and Dynamics in Relational Networks

These notes explore the use of Sydney Lamb’s relational network notion for linguistics to represent the logical structure of complex collection of attractor landscapes (as in Walter Freeman’s account of neuro-dynamics). Given a sufficiently large system, such as a vertebrate nervous system, one might want to think of the attractor net as itself being a dynamical system, one at a higher order than that of the dynamical systems realized at the neuronal level. A mind is a fluid attractor net of fractional dimensionality over a neural net whose behavior displays complex dynamics in a state space of unbounded dimensionality. The attractor-net moves from one discrete state (frame) to another while the underlying neural net moves continuously through its state space.

Parameter Estimation in Epidemiology: from Simple to Complex Dynamics.

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi‐strain dynamics to describe the virus‐host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

Bright points and ejections observed on the sun by the KORONAS-FOTON instrument TESIS

Five-second observations of the solar corona carried out in the FeIX 171 A line by the KORONAS-FOTON instrument TESIS are used to study the dynamics of small-scale coronal structures emitting in and around coronal bright points. The small-scale structures of the lower corona display complex dynamics similar to those of magnetic loops located at higher levels of the solar corona. Numerous detected oscillating structures with sizes below 10 000 km display oscillation periods from 50 to 350 s. The period distributions of these structures are different for P 150 s, which implies that different oscillation modes are excited at different periods. The small-scale structures generate numerous flare-like events with energies 1024–1026 erg (nanoflares) and with a spatial density of one event per arcsecond or more observed over an area of 4 × 1011 km2. Nanoflares are not associated with coronal bright points, and almost uniformly cover the solar disk in the observation region. The ejections of solar material from the coronal bright points demonstrate velocities of 80–110 km/s.

Exploring the composition of the recurrent neural activity accompanied with γ rhythm by injecting simulated complex conductance

Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.

Lessons from Jurassic Park: patients as complex adaptive systems

With realization that non-linearity is generally the rule rather than the exception in nature, viewing patients and families as complex adaptive systems may lead to a better understanding of health and illness. Doctors who successfully practise the 'art' of medicine may recognize non-linear principles at work without having the jargon needed to label them. Complex adaptive systems are systems composed of multiple components that display complexity and adaptation to input. These systems consist of self-organized components, which display complex dynamics, ranging from simple periodicity to chaotic and random patterns showing trends over time. Understanding the non-linear dynamics of phenomena both internal and external to our patients can (1) improve our definition of 'health'; (2) improve our understanding of patients, disease and the systems in which they converge; (3) be applied to future monitoring systems; and (4) be used to possibly engineer change. Such a non-linear view of the world is quite congruent with the generalist perspective.

On the use of stationary versus hidden Markov models to detect simple versus complex ecological dynamics

The stationary Markov model (SMM) has been used to study simple ecological dynamics, such as classic Clementsian succession towards a climax. There has been considerable dissatisfaction among ecologists, however, because succession has been found to display complex dynamics. The application of hidden Markov models (HMM) is proposed for two reasons: (1) they can have multiple states with observations that need not converge on a stable configuration and (2) the hidden states allow for the detection of underlying ecological processes. A comparative analysis is made between the well-known SMM and the lesser known HMM using a range of hypothetical species response types with concentration on the prediction of ecological observation sequences and the detection of underlying ecological processes. The HMM provides similar predictive ability to that of the SMM in the case of simple dynamics but shows considerably improved performance for complex dynamics. The HMM also provides increased interpretive capabilities by suggesting where transitions in underlying hidden states can be identified, even when not apparent in the observable dynamics.

Rocking Newton’s cradle

In textbook descriptions of Newton’s cradle, it is generally claimed that displacing one ball will result in a collision that leads to another ball being ejected from the line, with all others remaining motionless. Hermann and Schmälzle, Hinch and Saint-Jean, and others have shown that a realistic description is more subtle. We present a simulation of Newton’s cradle that reproduces the break-up of the line of balls at the first collision, the eventual movement of all the balls in phase, and is in good agreement with our experimentally obtained data. The first effect is due to the finite elastic response of the balls, and the second is a result of viscoelastic dissipation in the impacts. We also analyze a dissipation-free ideal Newton’s cradle which displays complex dynamics.

Sand Ripples Induced by Water Shear Flow in an Annular Channel

We have studied experimentally the formation and evolution of sand ripples under water shear flow in a narrow annular channel. The amplitude of the sediment ripples vanishes at a critical value of the shear rate. Near this onset, a band of Fourier modes can be described by exponential growth functions. The growth rates vary linearly with the shear rate. On longer times the sand ripples display complex dynamics.

Dynamics of the noisy neural network

The dynamic features of interspike interval sequences and structures of spatiotemporal patterns of firing in a coupled noisy neural network are investigated. The system displays complex dynamics under periodic external stimuli. The dynamics is modulated by a periodic impulse-like synaptic current which relates to a global coupling interaction between neurons. The firings of the stimulated neurons are phase-locked to this current. In addition, the interspike interval histograms are studied for the case of frozen noise which does not change its value within a time interval once it has been distributed onto the network. It is found that the peaks in these histograms are located at integer multiples of the period of the external stimulus, and the heights of these peaks decay exponentially, which corresponds to the experimental results.