Boundary Crisis Research Articles

Dynamical Control for the Parametric Uncertain Cancer Systems

In this study, we consider a parametric uncertain Lotka-Volterra cancer model including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The biological parameter (i.e., cell growth rate) is described as a form of the triangular fuzzy number. By using grade mean value conversion, the imprecise fuzzy parameter is translated into the degree of optimism (λ-integral value λ ∈ [0,1]) interval. We derive the sufficient conditions for the existence of the region of asymptotic stability (RAS) in the fuzzy cancer model. The boundary crisis of transient chaos and properties of RAS are investigated under fuzzy environment. We present a dynamical perturbation control to avoid uncontrolled tumor cell growth and prevent healthy cell extinction.

Complex aperiodic mixed mode oscillations induced by crisis and transient chaos in a nonlinear system with slow parametric excitation

For dynamic systems with multiple time scales, its long-term behaviors usually present as mixed mode oscillations (MMOs). The formation of MMOs is closely related to the fast transitions evoked by the bifurcations of the fast sub-system. Up till now, most of the results reported in deterministic systems focus on periodic MMOs, namely the holistic structure of waveform shows periodicity, no matter whether the slow manifolds that the fast–slow flow follows are periodic or not. Moreover, since the motion of the fast–slow flow is modulated by the critical manifolds, qualitative influences of transient behaviors on the holistic structure of MMOs are less concerned. While in this paper, three patterns of aperiodic MMOs are analyzed based on a three-dimensional nonautonomous system under slow parametric excitation. According to the types of manifolds among which the fast transitions take place, these MMOs can be named as aperiodic “cycle-chaos-cycle” MMOs, aperiodic “cycle-chaos-cycle” MMOs with additional chaotic bursters, and aperiodic “chaos-cycle-point” MMOs. By combining the fast–slow analysis on certain time intervals and the probe into the transient chaos near boundary crisis, generation mechanisms of these MMOs are investigated. Our results show that the relative location between the boundary crisis value and the minimum of slow variable will qualitatively change the pattern of large amplitude oscillations (LAOs); thus, the composition of bursters can be decided by the intensity of transient chaos. On the other hand, the small amplitude oscillations (SAOs) evoked by interior crisis may contain inner structures related to bifurcation delay and sharding phenomenon. Particularly, interior crisis can lead to merging phenomena of chaotic attractors. Thus, when the chaotic LAOs stages are over, the fast–slow flow can transit to upper or lower branch in a irregular way, which results in the uncertain locations of SAOs.

Sequence of Routes to Chaos in a Lorenz-Type System

This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos (n=1) and a sequence of sub-bifurcation routes with n=3,4,5,…,14 isolated sub-branches to chaos. When n is odd, the n isolated sub-branches are from a period-n limit cycle, followed by twin period-n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When n is even, the n isolated sub-branches are from twin period-n/2 limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.

Multistability Control of Hysteresis and Parallel Bifurcation Branches through a Linear Augmentation Scheme

Abstract Multistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua’s oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov’s exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable.

Evolution and paleobiogeography of mangroves

AbstractWe reviewed the geological record of mangroves based on fossil pollen, fruits, and wood evidence of Nypa, Avicennia, Sonneratia, Rhizophoraceae, and mangrove associates to trace the origin, distribution, extinction, and range contraction of paleo‐mangroves during the Late Cretaceous–Miocene time. Our study region covers paleocoastal areas of Indo‐West Pacific (IWP) and Atlantic East Pacific (AEP) region. First, we compiled the mangrove fossil records from the Late Cretaceous till Miocene and identified the migration pattern for Nypa, Avicennia, Sonneratia, Rhizophoraceae members, and mangrove associates such as Acrostichum, Wetherellia, Pelliciera, Aegiceras, Heritiera, Excoecaria, and Barringtonia. Second, we interpreted the paleoclimate shifts which caused the dispersal/extinction of this specialized ecosystem. Lastly, we proposed the future consequences of mangrove diversity for restoration and conservation strategies. First mangroves appeared during the Late Cretaceous, 100–65 Ma, since then their evolution is closely related to sea‐level changes in geological times. The oldest geological record of Nypa palm which prefers broad ecological tolerance is a good example for pantropical distribution of mangroves. High sea‐level and humid climate offered sufficient coastal regions and climate for the development of 12 genera of mangroves in nine families and subsequent proliferation into newer areas during early to middle Eocene (~50–40 Ma). The Eocene/Oligocene boundary crisis heralds the beginning of a biogeographical split between the present‐day eastern and western provinces of mangroves with records of Sonneratia, Rhizophora, Pelliciera, Barringtonia, and Acrostichum. However, during Oligocene and Middle Miocene mangroves occupied the present geographical position with addition of Nypa, Avicennia, and Excoecaria species. Re‐evaluation of Cenozoic records suggests that the climatic conditions of Late Paleocene, end of Eocene, and middle Pliocene were the driving force that led to the evolution and expansion of mangrove flora. During the Neogene, latitudinal contraction, extinction, and migration of mangroves led to the present bipartite distribution. The Himalayan uplift and establishment of Asian summer monsoon toward Late Neogene further affected the coastal dynamics which tailored the mangrove distribution of the Indian subcontinent. Loss of ecological habitats and local extinction forming disjunct distribution of mangroves during the Quaternary have also affected its overall biogeography.

A chaotic circuit under a new classification framework of inductorless Chua’s circuits

PurposeThis paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework.Design/methodology/approachIn this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter.FindingsCompared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor.Originality/valueThe newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.

Fourth international conference on recent advances in nonlinear mechanics RANM 2019

The authors took part in the work of the Fourth International Conference on Recent Advances in Nonlinear Mechanics that was holding in Poland, in Lodz in May 2019. They contributed the presentation titled “Observing the Intermittent Transition to Chaos in Vibroimpact System with Wavelet Transform Applying” by V.A. Bazhenov, O.S. Pogorelova, T.G. Postnikova. They told about watching the intermittency route to chaos and the boundary crisis in vibro-impact system with a small change in the control parameter. The presentation was illustrated by bright slides. The surfaces of wavelet coefficients and their projections show the system chaotic motion and intermittency very visibly and clearly.The conference was very representative, and many well-known prominent scientists from 23 countries attended the conference. 7 plenary lectures and 102 sectional reports were heard. Well-known distinguished scientists Professors Marian Wiercigroch (UK) and Przemyslaw Perlikowski (Poland) were the chairs of conference. The conference had some, we can say, engineering orientation. The reports often discussed important issues of nonlinear mechanics on examples of specific engineering objects. Almost all reports presented the section "Objectives and Motivation". Many experimental results were discussed.Unfortunately, there were only 4 participants from Ukraine, only 2 contributions were made by Ukrainian scientists themselves. But there were 4 contributions with a large number of famous co-authors from different countries and 2 co-authors from Ukraine among them. Poland as the hostess presented 43 reports and 104 participants. Of course, English was the work language and the language of communication.The conference was perfectly organized. The organizers held two wonderful excursions. There was excellent music interlude as Opening Ceremony. There was a great congratulation to the famous scientist Professor Tomasz Kapitaniak on his anniversary at the Conference Dinner.In the article, the authors share their impressions about the work of the conference.

Developments in the stratigraphy of the Deccan Volcanic Province, peninsular India

The Deccan Volcanic Province has been considered as one of the largest magmatic regions, involving an aerial coverage of ca. 500,000 km2. It is subdivided into four sub-provinces, and holds a unique position in global tectonic models for understanding earth's geodynamics and the impact of voluminous eruptions on the contemporary biosystem and climate system. Published stratigraphic data suggest that volcanic eruption took place from 69 to 64 million years (Ma) ago when the Indian plate passed over the Réunion hotspot. The main phase of volcanic activity consisting of about 80% of total basaltic lava, erupted rapidly, during a short span (<1 Ma) or even less (two or three hundred thousand years), close to chron 29R, straddling to the Cretaceous–Paleogene (K–Pg) boundary. Recent high-precision age data show that the main volcanic phase is genetically linked to the Chicxulub impact and plume-head of the hotspot, and largely contributed to the end-Cretaceous mass extinction. To assess the links of the province to the K–Pg boundary, Chicxulub impact, Réunion plume, and Late Cretaceous global climate crisis, it is crucial to have a current state of knowledge of the understanding of its stratigraphy. A review of published data shows a surge in the province research that has considerably advanced the understanding of its stratigraphy. This province is intercalated with numerous infra- and intertrappean sedimentary beds that have yielded diverse biota, providing a reliable relative time control for duration of the volcanic activity. This paper presents a review of the stratigraphic developments of the province (lithostratigraphy, chemostratigraphy, magnetostratigraphy, and chronostratigraphy) from the very beginning to the present, and discusses the role of the Réunion plume in its formation.

A direct transition to chaos in hysteretic systems with focus dynamics.

A specific transition to chaos is detected in the study of periodic orbits of hysteretic systems with symmetry and dynamics of focus type. The corresponding bifurcation is rigorously justified by resorting to the analysis of transition maps, whose mathematical expressions are adequately derived. It is shown that, depending on a parameter related to the location of equilibria, such transition maps can pass from being a smooth function to a discontinuous, piecewise-smooth function. We deal with the intermediate situation for which the transition map is continuous but nonsmooth. Using a second parameter, and previous known results on chaotic maps, we show in a rigorous way the existence of a chaos boundary crisis bifurcation, where the transition from a configuration without periodic orbits to another with bounded chaotic solutions occurs.

Study of Routes to Chaos in Vibroimpact System with Continuous Wavelet Transform

The study of dynamical systems chaotic behavior and their routes to chaos was in particular attention at recent years. These phenomena study in non-smooth dynamical system is of the special scientists’ interest. We apply the Continuous Wavelet Transform (hereinafter - CWT) to investigate the intermittent route to chaos, boundary crisis, and transitional regimes under quasi-periodic route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT application is very useful to observe the intermittency, chaos and transitional regimes. It allows one to detect and to determine these phenomena with great confidence, reliability, and clearness.

Are Late Permian carbon isotope excursions of local or of global significance?

Abstract We present a new, biostratigraphically calibrated organic and inorganic C-isotope record spanning the basal Late Permian to earliest Triassic from southern Guizhou (Nanpanjiang basin, South China). After fluctuations of a likely diagenetic overprint are removed, three negative carbon isotope excursions (CIEs) persist. These include a short-lived CIE during the early Wuchiapingian, a protracted CIE ending shortly after the Wuchiapingian–Changhsingian Boundary, and a third CIE straddling the Permian–Triassic boundary. Comparison of our new C-isotope record with others from the same basin suggests that influences of local bathymetry and of the amount of buried terrestrial organic matter are of importance. Comparison with other coeval time series outside of South China also highlights that only the negative CIE at the Permian–Triassic boundary is a global signal. These differences can be explained by the different volumes of erupted basalts between the Late Permian Emeishan and the younger Siberian large igneous provinces and their distinct eruptive modalities. Emeishan volcanism was largely submarine, implying that sea water was an efficient buffer against atmospheric propagation of volatiles. The equatorial position of Emeishan was also an additional obstacle for volatiles to reach the stratosphere and benefit from an efficient global distribution. Consequently, the local significance of these CIEs calls into question global correlations based on C-isotope chemostratigraphy during the Late Permian. The timing of the Late Permian Chinese CIEs is also not reflected in changes in species diversity or ecology, unlike the sudden and global Permian–Triassic boundary crisis and subsequent Early Triassic upheavals.

A dolomitization event at the oceanic chemocline during the Permian-Triassic transition: REPLY

The Permian-Triassic boundary (PTB) crisis caused major shortterm perturbations in ocean chemistry, as recorded by the precipitation of anachronistic carbonates. Here, we document for the first time a global dolomitization event during the Permian-Triassic transition based on Mg/(Mg + Ca) data from 22 sections with a global distribution representing shallow- to deep-marine environments. Ten of these sections show high Mg/(Mg + Ca) ratios bracketing the PTB, recording a short-term spike in dolomite formation. The dolomite consists mainly of micron-scale anhedral to subhedral crystals that are associated with abundant fossilized bacterial bodies and extracellular polymeric substances, suggesting that dolomite precipitation was induced by microbial metabolic activity. Sections showing a dolomite spike at the PTB are widely distributed geographically, but mostly encountered in mid-shelf to upper-slope settings. Because the dolomitization event coincided with a rapid expansion of oceanic anoxia and high rates of sulfate reduction, we hypothesize that it was triggered by enhanced microbial sulfate reduction within the oceanic chemocline.

Migration Wars in the Traditional Igbo Society and the Challenges of National Security: The Abakaliki Experience, 1800-1920

Traditionally, state formation was characterized with wars of different magnitude. The nature, types and causes of the war differed from one state to another. The Igbo nation was one of those areas that witnessed migratory wars arising from state formation, land dispute, slave raiding and boundary crises. Considering the fact that the Igbo history of origin underpins diverse integrations and accounts, one can say that some Igbo sub-groups at different times, fought different wars with one another in search of national homeland. The outcome of these wars underscores the migration and settlement that predated the Igbo nation before the 18^th century wars, particularly the Ezza that are scattered all over Nigeria. The continuous movement of these people and many other Igbo sub-groups has led to the intermittent wars that characterized Nigerian state. This manifested in boundary disputes between several Igbo groups with her neighbours such as Ikwo-Nsobo and Osopo of Cross River State, Izzi –Osopo and Yala of Cross River State and Mgbo-Igala of Benue State. Evidences of these wars translated into indigene/settlers’ question that tend to decimate Nigeria’s nation. Against this background therefore, this paper seeks to interrogate how war of migrations in the traditional Igbo societies have continued to challenge Nigeria’s national security. The position of this paper is that, war is a natural phenomenon that can still occur despite migration, but the inability of the National Boundary Adjustment Commission to embark on complete interstate boundary adjustment increases the volume of wars, thus, challenging the Nigeria’s national security. Hence, the paper concluded by arguing that wars that challenge Nigeria’s national security are man-made and could be avoided if the Nigerian state rises to take up her responsibilities.

Global analysis of crises in shape memory thin plate system

The unique global properties of shape memory alloy are mainly derived from the martensite phase transition and its inverse, which result from the change of temperature and external load. In this paper, the global characteristics of shape memory alloy thin plate system are analyzed with the temperature and harmonic excitation amplitude as control parameters. Based on the method of Poincare map, the complex crisis phenomenon of the system including the sudden change in number, size and type of attractors can be observed through the global multivalued bifurcation diagram. However, the specific crisis type is not clear, it is necessary to be analyzed from the global viewpoint. By computing the global diagram with the composite cell coordinate system method which constructs a composite cell state space by multistage division of the continuous phase space, the attractors, saddles and basins of attraction of the system can be obtained more accurately. The vivid evolutionary processes of the crisis phenomena of the system are illustrated, and it can be found that the system presents a complex global structure with amplitude and temperature changing. There exist two kinds of crises: one is the boundary crisis resulting from the collision between a chaotic/periodic attractor and a chaotic saddle within the basin boundary, which causes the attractor to vanish, and the other is the merging crisis caused by the collision of two or more attractors with the chaotic saddle within the basin boundary where a new chaotic attractor appears. When multiple attractors coexist in the system, the basin boundary may be smooth or fractal, and for any point at boundary, its small open neighborhood always has a nonempty intersection with three or more basins, which is known as Wada basin boundary. It is difficult to predict the dynamic behavior of the system accurately due to the fractal, the Wada-Wada, Wada-fractal and fractal-Wada basin boundary metamorphoses which can be observed along with the variation of temperature and amplitude through the composite cell coordinate system method, which owns a unique advantage in depicting basin boundary. Furthermore, the Wada property is displayed more clearly by refining specified region. The results of this paper provide a theoretical analysis tool for adjusting the dynamic response of shape memory alloy thin plate system and optimizing the deformation and vibration control of mechanical equipment through controlling temperature and excitation intensity.

Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

A dolomitization event at the oceanic chemocline during the Permian-Triassic transition

The Permian-Triassic boundary (PTB) crisis caused major shortterm perturbations in ocean chemistry, as recorded by the precipitation of anachronistic carbonates. Here, we document for the first time a global dolomitization event during the Permian-Triassic transition based on Mg/(Mg + Ca) data from 22 sections with a global distribution representing shallow- to deep-marine environments. Ten of these sections show high Mg/(Mg + Ca) ratios bracketing the PTB, recording a short-term spike in dolomite formation. The dolomite consists mainly of micron-scale anhedral to subhedral crystals that are associated with abundant fossilized bacterial bodies and extracellular polymeric substances, suggesting that dolomite precipitation was induced by microbial metabolic activity. Sections showing a dolomite spike at the PTB are widely distributed geographically, but mostly encountered in mid-shelf to upper-slope settings. Because the dolomitization event coincided with a rapid expansion of oceanic anoxia and high rates of sulfate reduction, we hypothesize that it was triggered by enhanced microbial sulfate reduction within the oceanic chemocline.

Multiple sulfur-isotopic evidence for a shallowly stratified ocean following the Triassic-Jurassic boundary mass extinction

The cause of the Triassic-Jurassic (Tr-J) boundary biotic crisis, one of the ‘Big Five’ mass extinctions of the Phanerozoic, remains controversial. In this study, we analyzed multiple sulfur-isotope compositions (δ33S, δ34S and δ36S) of pyrite and Spy/TOC ratios in two Tr-J successions (Mariental, Mingolsheim) from the European Epicontinental Seaway (EES) in order to better document ocean-redox variations during the Tr-J transition. Our results show that upper Rhaetian strata are characterized by 34S-enriched pyrite, low Spy/TOC ratios, and values of Δ33Spy (i.e., the deviation from the mass-dependent array) lower than that estimated for contemporaneous seawater sulfate, suggesting an oxic-suboxic depositional environment punctuated by brief anoxic events. The overlying Hettangian strata exhibit relatively 34S-depleted pyrite, high Δ33Spy, and Spy/TOC values, and the presence of green sulfur bacterial biomarkers indicate a shift toward to euxinic conditions. The local development of intense marine anoxia thus postdated the Tr-J mass extinction, which does not provide support for the hypothesis that euxinia was the main killing agent at the Tr-J transition. Sulfur and organic carbon isotopic records that reveal a water-depth gradient (i.e., more 34S-, 13C-depleted with depth) in combination with Spy/TOC data suggest that the earliest Jurassic EES was strongly stratified, with a chemocline located at shallow depths just below storm wave base. Shallow oceanic stratification may have been a factor for widespread deposition of black shales, a large positive shift in carbonate δ13C values, and a delay in the recovery of marine ecosystems following the Tr-J boundary crisis.

Crisis of the chaotic attractor of a climate model: a transfer operator approach

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are known to be characterised by a single or a pair of characteristic exponents crossing the imaginary axis. As a result, the approach of such bifurcations in the presence of noise can be inferred from the slowing down of the decay of correlations (Held and Kleinen 2004 Geophys. Res. Lett. 31 1–4). On the other hand, little is known about global bifurcations involving high-dimensional attractors with several positive Lyapunov exponents.It is known that the global stability of chaotic attractors may be characterised by the spectral properties of the Koopman (Mauroy and Mezić 2016 IEEE Trans. Autom. Control 61 3356–69) or the transfer operators governing the evolution of statistical ensembles. Accordingly, it has recently been shown (Tantet 2017 J. Stat. Phys. 1–33) that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second class of resonances, the unstable resonances, are responsible for the decay of correlations and mixing on the attractor. In the deterministic case, these cannot be expected to be affected by general boundary crises.Here, however, we give an example of a chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice-albedo feedback, is also active on the attractor. Finally, we discuss implications regarding response theory and the design of early-warning signals.

Correction to: The suppression of random parameter on the boundary crisis of the smooth and discontinuous oscillator system

There was a mix-up of Figs. 6+7 and 8+9 in the initial online publication. The original article has been corrected.

Transient chaos in the Lorenz-type map with periodic forcing.

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.