Chaotic Complex Research Articles

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

In this paper, we introduce a new chaotic complex nonlinear system and study its dynamical properties including invariance, dissipativity, equilibria and their stability, Lyapunov exponents, chaotic behavior, chaotic attractors, as well as necessary conditions for this system to generate chaos. Our system displays 2 and 4-scroll chaotic attractors for certain values of its parameters. Chaos synchronization of these attractors is studied via active control and explicit expressions are derived for the control functions which are used to achieve chaos synchronization. These expressions are tested numerically and excellent agreement is found. A Lyapunov function is derived to prove that the error system is asymptotically stable.

GEOLOGICAL EVOLUTION OF THE KOZIAKAS OPHIOLITIC COMPLEX (WESTERN THESSALY, GREECE)

The Koziakas ophiolitic complex is located in Western Thessaly and is interpreted as a dismembered ophiolite sequence, which overthrust the Western Thessaly Unit (WTU). The Koziakas basal Unit consists of sedimentary rocks and occupies the stratigraphically lowermost members of the WTU. The Ophiolitic Unit overthrust the WTU and consists, from bottom to top, of a well-developed ophiolitic melange, a sub-ophiolitic metamorphic sole, serpentinites, serpentinized peridotites, peridotites (harzburgite, lherzolite, plagioclase lherzolite), massive dolerites, massive basalts and pillow lavas interlayered with Mnrich radiolarites. The ophiolitic melange comprises a chaotic multicoloured complex of various rock fragments. A sparse network of gabbroic (locally rodingitized), plagiogranitic and doleritic dykes intrudes the mantle tectonites along two main cross-cutting directions: the first strikes NE-SW and dips 50o-70o to the NW, the second strikes N-S to NNW-SSE with a dip of about 65o-80o to the west. The dominant tectonic fabrics such as shear zones, fold axes, foliation planes and mineral streching lineations, imprinted mainly on the Koziakas mantle tectonites trend NW to NE and are consistent with a NE-SW emplacement direction. The similar radiometric ages and the comparable geological characteristics of the Koziakas ophiolitic complex with its adjacent ophiolite suites of Pindos, Vourinos and Othris imply that they probably developed in the same marginal basin represented by the Pindos ocean basin.

A Miocene Mud Volcano and Its Plumbing System: A Chaotic Complex Revisited (Monferrato, NW Italy)

ABSTRACT Chaotic deposits are frequently reported in the geological literature and are commonly interpreted as olistostromes or tectonic melanges. A chaotic complex in the Cenozoic succession of Monferrato (NW Italy) consists of interbedded mud breccia and burrowed silty clays that are pierced by sheared mud breccias and embed carbonate-cemented blocks. These may be represented by microcrystalline limestones or strongly cemented matrix-supported breccias locally containing remains of chemosymbiotic organisms (lucinid bivalves). Moreover, cylindrical concretions, up to 15 cm in diameter and 1 m long, occur in the chaotic complex and crosscut bedding planes at high angles. The cement of all these lithified portions is mainly dolomite characterized by low 13C values (from -10.3 to -23‰ PDB) and 18O values up to +7‰ PDB. The 13C values testify to precipitation of carbonates induced by microbial oxidation of methane, whereas the markedly positive 18O signature, ubiquitous in the cylindrical concretions, is the evidence for the presence and destabilization of gas hydrates. The studied section provides a well-exposed example of the geological record of the birth, life, and death of a mud volcano. Unsheared, soft mud breccias represent mud flows along the flanks of the volcano, whereas sheared mud breccias are the result of the injection of unconsolidated overpressured fine-grained sediments, both taking place during eruptive phases. They were followed by more quiet stages of hemipelagic sedimentation, burrowing, and CH4 seeping. The cylindrical concretions represent the first described ancient example of the chimneys observed in present-day mud-volcano settings. They are the remnants of a cold-seep plumbing network that crosscut the mud volcano edifice. The chimneys were the pathway for the expulsion toward the sea floor of gas- and sediment-charged fluids likely originated from destabilization of methane gas hydrates. The association of mud breccias and methane-derived carbonates may not be due to mass gravity flows but can be primary and, therefore, is a diagnostic criterion for recognizing chaotic deposits due to mud volcano activity in the geological record.

Raticosa Tunnel, Italy: Characterization of Tectonized Clay-Shale and Analysis of Monitoring Data and Face Stability

The Raticosa Tunnel (Italy) is one of several tunnels currently under construction for the new Bologna-Florence high-speed railway line. The tunnel, having an overburden of up to 500 m, is located in the Apennine range and half of its 10 km length crosses a tectonized clay-shale formation known as "Chaotic Complex". The construction method is based on full face excavation combined with face reinforcement by means of fiber-glass dowels. Primary lining consists of a shotcrete layer and closed-ring steel sets. Due to heavy squeezing ground conditions, as predicted in the preliminary investigation phase, the excavation of the tunnel was performed under the strict control of an extensive monitoring system. The paper presents an overview of the physical and mechanical parameters of the Raticosa shale, summarizing the results of laboratory and in situ tests. Face "extrusion" and tunnel wall displacements recorded during the excavation advance have been analyzed and correlated with construction stages. The displacements measured near the tunnel face generally confirm the validity of the design criteria of face reinforcement and early invert closure, which assures tunnel stability before casting the final lining. Large, time-dependent, deformations of ground have generally been recorded, causing local failure phenomena at some locations along the tunnel route. A tentative explanation of the observed behavior has been proposed on the basis of empirical models. Finally, the effect of fiber-glass dowels on face stability has been evaluated by using limit analysis.

DEFORMATION FEATURES WITHIN THE SESTOLA-VIDICIATICO UNIT: A POTENTIAL CASE HISTORY OF A FOSSIL EROSIVE SUBDUCTION CHANNEL AT THE SUBDUCTION-COLLISION TRANSITION

In the Northern Apennines the evolution of the frontal wedge during the Miocene transition from oceanic subduction to continental collision is preserved in an extensive chaotic complex or melange called the Sestola Vidiciatico Unit (SVU). The SVU is sandwiched between the Oligocene- Miocene foredeep deposits and the overlaying Ligurian oceanic units. These latter units represent an ancient accretionary prism build up during the closure of the Ligurian- Piedmontese oceanic basin. From the Oligocene to the Miocene time, the Ligurian prism progressively overthrust the thick silicoclastic turbidite sequences deposited in an outwards migrating foredeep-basin. The SVU is entirely composed of huge debris flow deposits, large blocks/chunks and slabs (up to few km in size) of the already deformed Ligurian or sub-Ligurian units preserving their original internal state of deformation, alternated with slices of various sizes of Upper Eocene-Lower Miocene slope apron deposits. Detailed structural analysis of all the different components of this melange shows that: – the contacts between the single components are usually structural; – the slope apron deposits do not show any evidence that they experienced shortening and contraction, they instead are pervasively sheared and cross-cut at all scales by sets of conjugate extensional mesoscopic faults, which have been originated before the complete lithification of the sandstone layers. Also the debris flow deposits and the blocks of the Ligurian units are split by extensional brittle mesoscopic faults sealed by shear calcite veins. In the footwall of the SVU the upper part of the foredeep deposits shows evidence of soft-sediment deformation originated at very high fluid pressure (repeated events of hydrofracturing) and is characterised by sets of conjugate extensional mesoscopic faults. Moving from SE to NW the SVU displays a clear change in composition as it recycles progressively more internal parts of the former Ligurian accretionary prism. At the same time, the epi-Ligurian sequence shows an initial stage of rapid uplift followed by a progressive deepening. From present-day active subduction zones we know that erosive margins are marked by three main characters: extension in the prism, progressive subsidence and transfer of material from the upper to the lower plate. The second and the third characters have been identified in SVU which may be considered a fossil analogue for subduction erosion if we compare the first stage of collision to the subduction of thick crust at an active margin that shift the mechanism from accretion to erosion.

The Parona chaotic complex: a puzzling record of the Messinian (Late Miocene) events in Monferrato (NW Italy)

The Parona chaotic complex (PCC) from Monferrato (NW Italy) is a mélange composed of carbonate-cemented blocks floating in a matrix of weakly consolidated mud breccias. It forms a minor (1 km 2) chaotic sedimentary body enclosed in a larger Messinian mélange that rests unconformably on older deposits and is followed, again unconformably, by Pliocene sediments. Three main facies have been recognized in the blocks. (a) Bioclastic rudstones and coquinoid grainstones of early Messinian age, composed of oligotypic assemblages of gastropods and the brackish-water bivalve Cerastoderma, mixed with shallow-water, marine biota (mollusks, corallinae algae, benthic foraminifers, echinoid fragments, rare ahermatypic corals). These sediments record shallow-water carbonate sedimentation with episodic brackish incursions and show a peculiar diagenetic overprint (selective dissolution of aragonitic grains and early dolomitic cements). (b) Monogenic breccias, composed of clasts of coquinoid grainstones floating in a dolomitic microcrystalline matrix. (c) Polygenic conglomerates, composed of rounded clasts of pre-Messinian pelagic sediments, of lower Messinian bioclastic carbonates and of Messinian evaporitic carbonates. Finally, a few blocks of strongly cemented micritic limestones, interpreted as methane-derived carbonates for the geochemical signature of the carbonate phases (strongly depleted in 13C), are present. The matrix enclosing the blocks is a mud breccia containing centimeter-sized clasts of marly sediments. Micropaleontological analyses have shown that lower Messinian and upper Tortonian planktic foraminifers are mixed with lower Miocene, Oligocene and Eocene forms. The PCC results from complex processes involving: (1) deposition of the peculiar sediments preserved in the blocks and (2) their dismemberment and mixing. As for the depositional history, composition of the blocks has allowed to sketch the following evolution. (a) Deposition of bioclastic rudstones and coquinoid grainstones that are interpreted as lower Messinian carbonate platform deposits for their strong compositional and diagenetical similarity with the lower Messinian carbonates cropping out in the Mediterranean region. The Monferrato bioclastic sediments are the northernmost example of Messinian shallow-water carbonates yet known. (b) Deposition of monogenic breccias. They formed during the evaporitic phase of the Messinian that was accompanied by a relative sea-level drop and by erosion of the previously deposited coquinas. Depositional and diagenetical processes during the evaporitic phase are also recorded by clasts of evaporitic carbonates in the polygenic conglomerates. (c) Deposition of polygenic conglomerates that are interpreted as upper Messinian post-evaporitic fan delta facies resulting from an important erosional phase. After deposition, this succession was dismembered in the blocks forming the present-day mélange. Geometry, stratigraphic relationships, and internal characteristics of the PCC point to an origin related to gravity-driven phenomena, triggered by tectonics. However, the faunal mixing in the mud breccias and the occurrence of blocks of methane-derived carbonates suggest that mud diapirism also played a role for the genesis of the PCC. This latter mechanism, which has been poorly considered until now, could also have been effective in the genesis of Messinian chaotic deposits that extensively crop out in NW Italy.

The Jurassic ophiolitic melange in the NE Dinarides: Dating, internal structure and geotectonic implications

A chaotic complex (Repno Complex) exposed in the Inner Dinarides, NW Croatia, consists of a mixture of magmatic and sedimentary rocks in a dark shaly matrix. It exhibits the typical features of ophiolitic melanges originating from subduction and accretionary processes. An Early Jurassic to Bajocian age of the fine-grained terrigenous sediments, now composing the shale matrix, is documented by palynomorph assemblages. Continental source areas with "eastern" affinities are envisaged for the shale matrix. The included bodies, millimetric to kilometric in size, consist of sandstones, cherts, red shales, pyroclastics, basalts, gabbro and ultramafics. The shale matrix shows a characteristic scaly cleavage. The preservation of the various inclusions depends on their rheological behaviour during accretion/subduction processes. The most mobile components were the fine-grained terrigenous sediments now represented by the shaly matrix. Subduction processes and formation of the melange developed between the Middle Jurassic and the Hauterivian. The relevant ocean segment was presumably closed before the Barremian. It is suggested that the Meliata, Repno and Central Dinaric oceanic domains were parts of the single ocean belt neighbouring the Adria.

Structural evolution of the early Miocene in the eastern Betic internal-external zone boundary (SE Spain)

Abstract The Internal-External Zone boundary (IEZB) in the eastern Betic Cordillera partially coincides with the Cadiz-Alicante Accident, mainly a major transcurrent fault of N060E direction. The study of an area located along the IEZB at a point where it separates from the Cadiz-Alicante accident has provided details concerning the geodynamic evolution of the cordillera at the moment of its structuration. Here the Internal Zone, consists of rocks assigned to the Malaguide Complex, dating its last sedimentation to the Aquitanian, and deposits assigned to the Vinuela Group (early-middle Burdigalian). The nappes of the Internal Zone were emplaced during the latest Aquitanian and the Vinuela Group (here the El Nino Formation) sealed it but was afterwards affected by the collision with the External Zone. On the other side of the boundary, the External Zone comprises two tectonic units: the Penarrubia Unit (late Cretaceous-middle Burdigalian), which is made up mainly of limestones and marls, and the El Frances Chaotic Complex composed by a set of different lithologies, all from the External Zone in a marly matrix that could be interpreted as a collisional melange formed in the early-middle Burdigalian. The contact between the two domains corresponds to a backthrust of the External Zone over the Internal Zone which occurred in the middle Burdigalian. The deposits sealing the IEZB are dated by calcareous nannofossils and planktonic foraminifera as late Burdigalian, and comprise clasts from both domains.

Stability evolution of clayey slopes and measurement modelling of mobilizing shearing resistance

Materials in black clays weakly silty of the chaotic complex of “Argille Scagliose” and in blue clays with silt and weakly sandy of the basin of the Upper Pliocene, in the Bologna area (Italy) were examined.Samples with a different saturation degree for considering significant elastic modulus and permeability coefficients characteristic of homogeneous real unities of slope were tested. With these data it was possible to perform direct shearing resistance measurements with parameters expressed in effective and residual terms, to anlyse the stability of slopes formed with different materials and in evolutionary configuration of erosion.The permeability of these materials measured direct in the country, is about 10−4 cm.s−1 for blue clay and 10−5 cm.s−1 for black clay. In the laboratory in connection with homogeneous samples, permeability reaches values of 10−8 cm.s−1 for both materials.The subsequent tests of shear resistance carried out with the construction of a special speed reducer utilized three different speeds of preconstituted shear, i.e.: 10−3 cm.s−1, 10−5 cm. s−1, 10−7 cm.s−1. These tests have put in evidence higher values of shear resistance for blue clays with respect to black clays which reach lower values for the shear speed of 10−7 cm.s−1. This shear speed was chosen because it allows an almost complete dissipation of pore pressure. The axial compression tests with lateral deformation in free air revealed different elastic moduli for saturated and nonsaturated samples and for the two different materials tested. In particular: the elastic modulus for blue clays is smaller than that for black clays whereas saturated samples have an elastic modulus greater than that for non saturated samples. These data, introduced in a finite element model that utilises triangular mesh with at least six nodes, were analysed with the automatic system of calculation of plasticity with axis symmetric produced from “Plaxis”.With erosional data collected monthly and annually, projected to 100 and 300 years, a slope erosional model was constructed that made it possible to verify that black clays are unstable with Fs passing from 0.98 to 0.95 over 100 years. It is also possible to see that blue clays move towards stability with Fs passing from l.32 to l.34 over 100 years and to l.39 over 300 years.

Chaotic complex spreading sequences for asynchronous DS-CDMA. Part II. Some theoretical performance bounds

For pt.I see G. Mazzini et al., vol.44, pp.937-47 (Oct. 1997). This paper and its companion (Part I) are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous Code Division Multiple Access. In Part I, a performance index was introduced and exploited to a priori estimate the performance of DS-CDMA communications systems based on chaotic spreading sequences, and to compare it to that of conventional systems. Here, tools from nonlinear dynamical system theory are employed to give a formal ground for those results. Analytical bounds on the expected partial cross correlation between spreading sequences obtained by quantizing and repeating a chaotic time series are derived, ensuring general applicability of such a technique in a real environment. Further analytical arguments guarantee that, when particular chaotic generators are used, expected performance is not worse than that of a well-behaving communications system. This analysis ensures also that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth.

Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results

This paper and its companion are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous code division multiple access. Sequences obtained by repeating a truncated and quantized chaotic time series are compared with classical m-sequences and Gold sequences by means of a performance index taken from communication theory which is here defined and thoroughly discussed. This analysis reveals that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth. Numerical simulations are reported, showing that systems based on chaotic spreading sequences perform generally better than the conventional ones. Some analytical tools easing the comprehension of these advantages are summarized.

The pH influence on the index properties of clays

Three clay sediments, concerning Pliocenic clay, Chaotic Complex clay and commercial kaolinic clay, have been studied in order to verify the pH influence on the index properties. The analysed clays have been mineralogically characterized in natural, conditions, and in modified pH conditions. This last procedure, obtained respectively by adding NH4OH or CH3COOH 1 mol., in a pH range between 4.5–11.3 has been carried out. To verify the different experimental conditions the C.E.C. of exchangeable cations as K+, Na+, Ca++ and Mg++, has been measured. The index properties obtained show a different behaviour of the three clays. The kaolin is not much affected only a limited WL% increase is recognizable when the pH decreases. The Chaotic complex clay evidence a considerable rise of the WL with the pH uncrease. In the Pliocenic clay the WL value increased with the pH. The described process can be related to the natural environment, connected also with various pollution phenomena.

Kurosegawa terrane: disrupted remnants of a low latitude Paleozoic terrane accreted to SW Japan

The Kurosegawa terrane is an anomalous, disrupted, predominantly Paleozoic lithotectonic assemblage of convergent continental margin affinity located between two Mesozoic terranes in SW Japan. On the basis of Silurian macrofossils in limestones and sparse Devonian plant fossils in overlying volcaniclastic sediments portions of the terrane were considered previously to represent a Silurian through Devonian sedimentary succession. Radiolarian data, together with sedimentological analysis, indicate the possibility that hiatuses may occur in this succession although their position remains indeterminate. Faunal, floral and paleomagnetic data indicate low latitude development during the Paleozoic, probably near the northern margins of Gondwana. Late Paleozoic oceanic crustal rocks are incorporated in a chaotic complex which crops out along the northern margin of the terrane. The chaotic rocks are interpreted to represent remnants of a subduction complex. Spatial relations of weakly-metamorphosed subduction complex rocks distributed along the northern side of the terrane and higher grade blueschist-bearing rocks to the south may indicate that during the Late Paleozoic to Early Mesozoic, subduction was south-directed along the northern margin of the Kurosegawa terrane. In the Jurassic, the Kurosegawa terrane underwent an oblique collision with Japan which was then part of Eurasia. Strike-slip faulting, associated with, and post-dating this collision resulted in dispersal of the Kurosegawa terrane into a narrow, discontinuous belt which transects the outer zone of SW Japan.

Chaotic complex dynamics and Newton's method

We consider one-parameter families of Julia sets arising from Newton's method in the complex domain. We show the existence of bifurcation points where zeros coalesce or change from attractors to repellors, and points where chaotic behavior occurs.